• Math Article

## Number System

The number system or the numeral system is the system of naming or representing numbers. We know that a number is a mathematical value that helps to count or measure objects and it helps in performing various mathematical calculations. There are different types of number systems in Maths like decimal number system, binary number system, octal number system, and hexadecimal number system. In this article, we are going to learn what is a number system in Maths, different types, and conversion procedures with many number system examples in detail .  Also, check mathematics for grade 12 here.

## What is Number System in Maths?

A number system is defined as a system of writing to express numbers. It is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner. It provides a unique representation of every number and represents the arithmetic and algebraic structure of the figures. It also allows us to operate arithmetic operations like addition, subtraction, multiplication and division.

The value of any digit in a number can be determined by:

• Its position in the number
• The base of the number system

Before discussing the different types of number system examples, first, let us discuss what is a number?

## What is a Number?

A number is a mathematical value used for counting or measuring or labelling objects. Numbers are used to performing arithmetic calculations.  Examples of numbers are natural numbers, whole numbers, rational and irrational numbers, etc. 0 is also a number that represents a null value.

A number has many other variations such as even and odd numbers, prime and composite numbers. Even and odd terms are used when a number is divisible by 2 or not, whereas prime and composite differentiate between the numbers that have only two factors and more than two factors, respectively.

In a number system, these numbers are used as digits. 0 and 1 are the most common digits in the number system, that are used to represent binary numbers. On the other hand, 0 to 9 digits are also used for other number systems. Let us learn here the types of number systems.

## Types of Number Systems

There are various types of number systems in mathematics. The four most common number system types are:

• Decimal number system (Base- 10)
• Binary number system (Base- 2)
• Octal number system (Base-8)
• Hexadecimal number system (Base- 16)

Now, let us discuss the different types of number systems with examples.

## Decimal Number System (Base 10 Number System)

The decimal number system has a base of 10 because it uses ten digits from 0 to 9. In the decimal number system, the positions successive to the left of the decimal point represent units, tens, hundreds, thousands and so on. This system is expressed in decimal numbers . Every position shows a particular power of the base (10).

Example of Decimal Number System:

The decimal number 1457 consists of the digit 7 in the units position, 5 in the tens place, 4 in the hundreds position, and 1 in the thousands place whose value can be written as:

(1×10 3 ) + (4×10 2 ) + (5×10 1 ) + (7×10 0 )

(1×1000) + (4×100) + (5×10) + (7×1)

1000 + 400 + 50 + 7

## Binary Number System (Base 2 Number System)

The base 2 number system is also known as the Binary number system wherein, only two binary digits exist, i.e., 0 and 1. Specifically, the usual base-2 is a radix of 2. The figures described under this system are known as binary numbers which are the combination of 0 and 1. For example, 110101 is a binary number.

We can convert any system into binary and vice versa.

Write (14) 10 as a binary number.

Base 2 Number System Example

∴ (14) 10 = 1110 2

## Octal Number System (Base 8 Number System)

In the octal number system , the base is 8 and it uses numbers from 0 to 7 to represent numbers. Octal numbers are commonly used in computer applications. Converting an octal number to decimal is the same as decimal conversion and is explained below using an example.

Example: Convert 215 8 into decimal.

215 8 = 2 × 8 2 + 1 × 8 1 + 5 × 8 0

= 2 × 64 + 1 × 8 + 5 × 1

= 128 + 8 + 5

## Hexadecimal Number System (Base 16 Number System)

In the hexadecimal system, numbers are written or represented with base 16. In the hexadecimal system, the numbers are first represented just like in the decimal system, i.e. from 0 to 9. Then, the numbers are represented using the alphabet from A to F. The below-given table shows the representation of numbers in the hexadecimal number system .

Number System Chart

In the number system chart, the base values and the digits of different number systems can be found. Below is the chart of the numeral system.

## Number System Conversion

Numbers can be represented in any of the number system categories like binary, decimal, hexadecimal, etc. Also, any number which is represented in any of the number system types can be easily converted to another. Check the detailed lesson on the conversions of number systems to learn how to convert numbers in decimal to binary and vice versa, hexadecimal to binary and vice versa, and octal to binary and vice versa using various examples.

With the help of the different conversion procedures explained above, now let us discuss in brief about the conversion of one number system to the other number system by taking a random number.

Assume the number 349. Thus, the number 349 in different number systems is as follows:

The number 349 in the binary number system is 101011101

The number 349 in the decimal number system is 349.

The number 349 in the octal number system is 535.

The number 349 in the hexadecimal number system is 15D

## Number System Solved Examples

Convert (1056) 16 to an octal number.

Given, 1056 16 is a hex number.

First we need to convert the given hexadecimal number into decimal number

= 1 × 16 3 + 0 × 16 2 + 5 × 16 1 + 6 × 16 0

= 4096 + 0 + 80 + 6

= (4182) 10

Now we will convert this decimal number to the required octal number by repetitively dividing by 8.

Therefore, taking the value of the remainder from bottom to top, we get;

(4182) 10 = (10126) 8

Therefore,

(1056) 16 = (10126) 8

Convert (1001001100) 2 to a decimal number.

(1001001100) 2

= 1 × 2 9 + 0 × 2 8 + 0 × 2 7 + 1 × 2 6 + 0 × 2 5 + 0 × 2 4 + 1 × 2 3 + 1 × 2 2 + 0 × 2 1 + 0 × 2 0

= 512 + 64 + 8 + 4

Convert 10101 2 into an octal number.

10101 2 is the binary number

We can write the given binary number as,

Now as we know, in the octal number system,

Therefore, the required octal number is (25) 8

Convert hexadecimal 2C to decimal number.

We need to convert 2C 16  into binary numbers first.

2C → 00101100

Now convert 00101100 2 into a decimal number.

101100 = 1 × 2 5  + 0 × 2 4 + 1 × 2 3  + 1 × 2 2  + 0 × 2 1 + 0 × 2 0

= 32 + 8 + 4

## Number System Questions

• Convert (242) 10 into hexadecimal. [ Answer: (F2) 16 ]
• Convert 0.52 into an octal number. [ Answer: 4121]
• Subtract 1101 2 and 1010 2 . [ Answer: 0010]
• Represent 5C6 in decimal. [ Answer:  1478]
• Represent binary number 1.1 in decimal. [ Answer: 1.5]

Also Check: Binary Operations

## Computer Numeral System (Number System in Computers)

When we type any letter or word, the computer translates them into numbers since computers can understand only numbers. A computer can understand only a few symbols called digits and these symbols describe different values depending on the position they hold in the number. In general, the binary number system is used in computers. However, the octal, decimal and hexadecimal systems are also used sometimes.

## More Topics Related to Number Systems

Frequently asked questions on number system, what is number system and its types.

The number system is simply a system to represent or express numbers. There are various types of number systems and the most commonly used ones are decimal number system, binary number system, octal number system, and hexadecimal number system.

## Why is the Number System Important?

The number system helps to represent numbers in a small symbol set. Computers, in general, use binary numbers 0 and 1 to keep the calculations simple and to keep the amount of necessary circuitry less, which results in the least amount of space, energy consumption and cost.

## What is Base 1 Number System Called?

The base 1 number system is called the unary numeral system and is the simplest numeral system to represent natural numbers.

## What is the equivalent binary number for the decimal number 43?

How to convert 30 8 into a decimal number.

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## Number System.

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## Is AT&T down? Reports of nationwide outages may also be impacting Verizon and T-Mobile

Couldn’t make a phone call this morning?

Customers with cellular service through AT&T may be impacted by massive nationwide outages, which could also be impacting Verizon and T-Mobile users, according to Downdetector, a real-time outage monitoring website.

T-Mobile claimed there were no outages this morning, according to a statement.

Customers are seeing SOS only where service bars usually appear on their devices. Here's what that means.

## AT&T wireless service restored Thursday afternoon

AT&T said they have "restored wireless service to all our affected customers," according to a 2:10 p.m. CT network update on their website . "We sincerely apologize to them. Keeping our customers connected remains our top priority, and we are taking steps to ensure our customers do not experience this again in the future."

## What time did the AT&T outage happen?

According to Downdetector , more than 30,000 outages were reported at 3:29 a.m. ET this morning. By 6:59 a.m. ET, there were up to 71,000 outages.

## Why is my phone on SOS only?

When a user's cell phone isn’t connected to a cellular network, they will typically alert the user by giving an indication in the phone's status bar. Those notifications usually say “No Service” or “Searching,” but your phone may also say “SOS” or “SOS only.” When your phone goes into SOS mode, it can still make emergency calls.

## AT&T outage map

AT&T allows users to sign up for text alert updates about outages, or you can check on  outages with your mobile phone or internet here .

## How to check for Verizon outages

Verizon requires customers to sign into their accounts  to check outages , but you can also find troubleshooting info and check on the status of repair requests.

## T-Mobile says they had no outages

Through a statement via email, T-Mobile said, "We did not experience an outage. Our network is operating normally. Down Detector is likely reflecting challenges our customers were having attempting to connect to users on other networks."

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## AT&T says service is restored for all users after widespread outage Thursday

AT&T says it has restored service to all customers after tens of thousands were affected by a nationwide telecommunication outage Thursday morning.

At the disruption's peak, between 8 and 9 a.m. ET, more than 70,000 AT&T customers were reporting outages, according to Downdetector , a tracking site. By 2 p.m., outage reports had dwindled to fewer than 5,000.

"We have restored wireless service to all our affected customers. We sincerely apologize to them," AT&T said in a statement. "We are taking steps to ensure our customers do not experience this again in the future.

The company did not share information on why the outage may have started, or how many customers were affected. The outage figures reported by Downdetector, largely based on submissions from users , may not be accurate.

ABC News reported that federal officials found "no indications of malicious activity," quoting from a confidential memo the network had obtained. The memo reportedly reflected an assessment by the U.S. Cybersecurity and Infrastructure Security Agency (CISA), a federal agency that monitors cyber threats.

Officials at the federal agency did not confirm or refute the television network's account.

“CISA is aware of the reports and we are working closely with AT&T to understand the cause of the outage and its impacts, and stand ready to offer any assistance needed,” said Eric Goldstein, CISA executive assistant director for cybersecurity, in a statement.

The Federal Bureau of Investigation and Department of Homeland Security are working with the tech industry to help investigate the cause of the outage, John Kirby, the White House's national security communications adviser, told reporters.

He said the Federal Communications Commission has been in touch with AT&T, which he said was the only telecommunication network that hadn’t been fully restored.

“The bottom line is, we don’t have all the answers,” Kirby said. “We're being told that AT&T has no reason to think that this was a cyber-security incident. But again, I want to be careful. We won't know until an investigation has been completed.”

Kirby said the outage had an impact on Commerce Department operations but downplayed the disruption. “I don’t think it was crippling,” he said.

Along with the problems at AT&T, over 10,000 Cricket Wireless customers also reported outages.

USA TODAY has reached out to AT&T for more information.

What does SOS mode on iPhone mean? Symbol appears during AT&T outage Thursday

Wi-Fi calling: Can you make calls using Wi-Fi while AT&T is down? What to know amid outage

## Outages impact EMS

The outages impacted essential public services , including people’s ability to call emergency responders.

The Charlotte-Mecklenburg Police Department in North Carolina said in a post on X it was aware of the outages and that “customers were briefly unable to contact 9-1-1.” In Nevada, the Lyon County emergency communications center asked locals not to call 911 with an AT&T device and, instead, “call from a different service provider.”

In Philadelphia, the emergency management agency said just after 5 a.m. that the “nationwide outage was impacting all city-issued cell phones.”

## Verizon, T-Mobile say operations are normal

Verizon and T-Mobile each said services were operating normally, despite earlier reports of outages.

"Some customers experienced issues this morning when calling or texting with customers served by another carrier," a Verizon spokesperson told USA TODAY just after 8 a.m. ET. "We are continuing to monitor the situation."

"We did not experience an outage. Our network is operating normally," T-Mobile said in an emailed statement to USA TODAY. "Down Detector is likely reflecting challenges our customers were having attempting to connect to users on other networks."

Are landlines going extinct? Phone companies want to eliminate traditional landlines. What's at stake and who loses?

## Affected cellphone users vent on social media, while others gloat

Affected cellphone users took to social media to vent their frustration.

"Waking up happy, then opening my phone to see 'SOS only,' wrote one X user named Halli . She didn't specify her cellphone service. Another X user posted footage of a car crash beneath the message , "me going to work without Apple or Google maps."

Some customers on rival services seized the occasion to gloat. Broadcaster Kayla Braxton posted a GIF on X, showing someone relaxing on a swing while the landscape burns behind them, beneath the message, "Me with Verizon while everyone on my timeline with AT&T is losing their freaking minds."

Analysts predict AT&T will have to make amends when the outage is over.

"We expect that AT&T will offer some type of refund to restore customer goodwill," said Dave Heger , a senior analyst at Edward Jones. "We think that this type of outage can negatively impact financial results in the quarter in which it occurs and cause short-term lost goodwill with customers.  However, it does not have a longer-term impact on the business."

AT&T stock was trading slightly lower Thursday afternoon, down about 2% on the day.

## SOS symbol affecting AT&T users on iPhone

An SOS symbol appeared on the screens of some affected iPhone users with AT&T, where cell service bars are normally shown.

An SOS symbol on your phone means there is a cellular network "available for emergency calls," Apple's support website states.

"When you make a call with SOS, your iPhone automatically calls the local emergency number and shares your location information with emergency services," according to Apple. "In some countries and regions, you might need to choose the service that you need."

After making an emergency call, your iPhone alerts any emergency contacts designated in your phone.

Apple says all iPhone models 14 or later can also use Emergency SOS via satellite to text emergency services  when no cellular and Wi-Fi coverage is available.

-- Contributing: Joey Garrison

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## CBP Releases January 2024 Monthly Update

WASHINGTON — U.S. Customs and Border Protection (CBP) released operational statistics today for January 2024. Migrant encounters along the southwest border were significantly lower than experienced in December. CBP monthly reporting can be viewed on CBP’s Stats and Summaries webpage .

“As a result of seasonal trends, as well as enhanced enforcement efforts by the men and women of CBP and our international partners, southwest border encounters between ports of entry dropped by 50% in January. We continue to experience serious challenges along our border which surpass the capacity of the immigration system,” said Troy A. Miller, Senior Official Performing the Duties of the Commissioner. “CBP remains on the frontline in preventing fentanyl and other dangerous drugs from entering our country, enforcing our nation’s laws and interdicting 34% more fentanyl and 68% more cocaine than the previous month.”

CBP continues to work closely with U.S. Immigration and Customs Enforcement and U.S. Citizenship and Immigration Services to quickly process individuals encountered at the border and remove those who do not establish a legal basis to remain in the United States, utilizing consequences strengthened by the Circumvention of Lawful Pathways Rule.  Since May 12, 2023 to January 31, 2024, DHS has removed or returned over 520,000 individuals, the vast majority of whom crossed the southwest border, including more than 87,000 individual family members. The majority of all individuals encountered at the southwest border over the past three years have been removed, returned, or expelled.  Total removals and returns since mid-May exceed removals and returns in every full fiscal year since 2013.

Below are key operational statistics for CBP’s primary mission areas in January 2024. View all CBP statistics online.

Ensuring Border Security and Managing Migration

CBP has taken significant steps to surge personnel and resources to impacted areas and address challenges we have experienced across the southwest border. CBP continues to expeditiously process and remove individuals who do not have a legal basis to remain in the country. We are working together with our domestic and foreign partners to jointly limit disorderly migration across the region, offering lawful pathways and cutting out ruthless smugglers who continue to spread falsehoods and show disregard for the safety and well-being of vulnerable migrants. CBP is targeting and disrupting transnational criminal organizations and smugglers who take advantage of and profit from migrants.

In January 2024, the U.S. Border Patrol recorded 124,220 encounters between ports of entry along the southwest border, a decrease of 50% from December 2023.

CBP’s total encounters along the southwest border in January 2024 were 176,205, a decrease of 42% from December 2023. Total encounters include U.S. Border Patrol encounters between ports of entry, as well as individuals who presented themselves at ports of entry (including those with CBP One appointments, detailed further below).

Among CBP’s 176,205 total southwest border encounters in January 2024, encounters with single adults decreased by 35% compared to December 2023, encounters with unaccompanied children decreased by 37% , and encounters with family unit individuals decreased by 51% .

CBP continually analyzes and responds to changes in migration patterns, particularly irregular migration outside of legal pathways and border crossings. We work with our federal and international partners to combat human smuggling. The fact remains: the United States continues to enforce immigration law, and our borders are not open for those without a legal basis to enter the country. Migrants attempting to enter without authorization are subject to removal under Title 8 authorities.

CBP’s message for anyone who is thinking of attempting to circumvent lawful pathways to enter the United States is simple: don’t do it. When noncitizens cross the border unlawfully, they put their lives in peril. The U.S. Border Patrol has undertaken significant efforts in recent years to expand capacity to aid and rescue individuals in distress. To prevent the loss of life, CBP initiated a Missing Migrant Program in 2017 that locates noncitizens reported missing, rescues individuals in distress, and reunifies decedents’ remains with their families in the border region. In January, the U.S. Border Patrol conducted 245 rescues, totaling 1,611 rescues in FY 2024 .

View more migration statistics and rescues statistics .

CBP One™ App

The CBP One™ mobile application remains a key component of DHS’s efforts to incentivize noncitizens to use lawful, safe, humane, and orderly pathways and disincentivize attempts to cross between ports of entry. In January, CBP processed approximately 45,000 individuals through appointments at ports of entry utilizing advanced information submitted in CBP One™

CBP One appointments accounted for 87% of noncitizens processed at ports of entry;  demonstrating that noncitizens will follow an orderly process when one is available. Since the appointment scheduling function in CBP One™ was introduced in January 2023 through the end of January 2024, 459,118 individuals have successfully scheduled appointments to present at ports of entry using CBP One™  instead of risking their lives in the hands of smugglers. The top nationalities who have been processed are Venezuelan, Mexican, and Haitian.

A percentage of daily available appointments are allocated to the earliest registered CBP One™ profiles, so noncitizens who have been trying to obtain appointments for the longest time will be prioritized. CBP is continually monitoring and evaluating the application to ensure its functionality and guard against bad actors.

CHNV Parole Processes

Through the end of January 2024, over 357,000 Cubans, Haitians, Nicaraguans, and Venezuelans arrived lawfully and were granted parole under the parole processes. Specifically, over 75,000 Cubans,  144,000 Haitians,  64,000 Nicaraguans, and  92,000 Venezuelans were vetted and authorized for travel; and over  74,000 Cubans,  138,000 Haitians,  58,000 Nicaraguans, and  86,000 Venezuelans arrived lawfully and were granted parole.

As Safeguarding Communities by Interdicting Narcotics and Dangerous Drugs

As the largest law enforcement agency in the United States, CBP is uniquely positioned to detect, identify, and seize illicit drugs before they enter our communities. CBP’s combination of interdiction and intelligence capabilities, complemented by its border search authorities, scientific services, non-intrusive inspection equipment, and canine detection teams, places it at the forefront of the U.S. government’s efforts to combat illicit fentanyl and other dangerous drugs.

CBP continues to conduct operations, including Operation Apollo, which target the smuggling of illicit fentanyl and other dangerous drugs. These operations leverage intelligence and investigative information to target drug traffickers’ supply chains and interdict items required in the production of illicit fentanyl, including precursor chemicals, pill presses and parts, movement of finished product, and illicit proceeds.

Nationwide in January, fentanyl seizures increased 34% and cocaine seizures increased 68% from December to January.

To date in FY 2024 through January, CBP has seized 7,000 pounds of fentanyl. CBP has stopped more fentanyl in the last two years than in the previous five years combined, and we continue to optimize our intelligence and field operations to stop these deadly substances from reaching American communities.

Additional CBP drug seizure statistics can be found on the Drug Seizure Statistics webpage .

Facilitating Lawful Trade and Travel and Promoting Economic Security

As international travel continues to increase, CBP is leveraging technology to streamline efficiency and increase security at air and land ports of entry. Travelers are encouraged to utilize CBP’s mobile apps to enhance their travel experience, including the Global Entry Mobile Application and Mobile Passport Control , as well as new Global Entry Touchless Portals at nearly all international airports across the United States, which protect passenger privacy and expedite arrival processing by eliminating paper receipts.

Travelers arriving by air into the United States increased 14% from January 2023 to January 2024, and pedestrians arriving by land at ports of entry increased 2.6% over the same period.

CBP works diligently with the trade community and port operators to ensure that merchandise is cleared as efficiently as possible and to strengthen international supply chains and improve border security. In January 2024, CBP processed more than 2.7 million entry summaries valued at more than \$267 billion , identifying estimated duties of nearly \$7 billion to be collected by the U.S. government. In January, trade via the ocean environment accounted for 44% of the total import value, followed by air, truck, and rail.

Consumers are encouraged to be alert to the dangers of counterfeit goods especially when shopping online as they support criminal activity, hurt American businesses, and often have materials or ingredients that can pose serious health and safety risks. Every year CBP seizes millions of counterfeit products worth billions of dollars had they been genuine. In January, CBP seized 1,814 shipments that contained counterfeit goods valued at more than \$718 million . More information about CBP’s intellectual property rights enforcement is available at https://www.cbp.gov/trade .

View more travel statistics , and trade statistics .

Protecting Consumers and Eradicating Forced Labor from Supply Chains

CBP continues to lead U.S. government efforts to eliminate goods from the supply chain made with forced labor from the Xinjiang Uyghur Autonomous Region of China. In January, CBP stopped 424 shipments valued at more than \$236 million for further examination based on the suspected use of forced labor.

Intellectual property rights violations continue to put America’s innovation economy at risk. Counterfeit and pirated goods threaten the competitiveness of U.S. businesses, the livelihoods of American workers, and the health and safety of consumers.

View more UFLPA enforcement statistics , and intellectual property rights enforcement statistics.

Defending our Nation’s Agricultural System

Through targeting, detection, and interception, CBP agriculture specialists work to prevent threats from entering the United States.

CBP issued 6,248 emergency action notifications for restricted and prohibited plant and animal products entering the United States in January 2024. CBP conducted 102,987 positive passenger inspections and issued 898 civil penalties and/or violations to the traveling public for failing to declare prohibited agriculture items.

View more agricultural enforcement statistics .

U.S. Customs and Border Protection is the unified border agency within the Department of Homeland Security charged with the comprehensive management, control, and protection of our nation’s borders, combining customs, immigration, border security, and agricultural protection at and between official ports of entry.

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## Calais people-smuggling gang broken up with 19 arrests, says Europol

Year-long investigation leads to arrests of Iraqi Kurdish gang leader and five key organisers in Germany

One of the most active and largest people-smuggling gangs operating in Calais has been dismantled with 19 arrested by German, French and Belgian police after a year-long investigation, Europol has announced.

Operation Task Force Wave, involving 600 police, arrested the leader of the Iraqi Kurdish gang and five of the main organisers in Germany where the people-smuggling operation was orchestrated, police said.

The swoop on numerous addresses comes less than two months after five people drowned in Wimereux , a resort close to Calais, attempting to cross the Channel during freezing temperatures in early January.

Among the arrests were five “high value” targets or people in controlling roles in the gang.

Details of the investigation also lift the lid on how people-smuggling around Calais has been so successful, with almost 30,000 men, women and children crossing the Channel last year despite the risk of death.

Cheap dinghies were imported from China and transported into Germany through a complex operation involving surveillance by the gangs and rest areas in Belgium , where the smugglers would wait with the boats until given the order to head to Calais.

Premises in 28 locations were raided in Germany, with 12 boats, 179 life vests and 81 floatation devices for children seized along with 11 outboard motors, 10 engines and almost 60 electronic devices and a number of firearms.

The suspects were all based in Germany and are being detained under Belgian and French judicial orders.

Europol said: “The investigative activities, initiated at the end of 2022, identified the structure and modi operandi of this large criminal network, made up of Iraqi and Syrian nationals of Kurdish origin.”

Europol said the suspects “had set up their own logistical infrastructure with specific branches in charge of organising delivery of large amounts of nautical equipment” from China and into the EU via Turkey and on to France .

Drivers typically transported eight boats at a time with “a forerunner car” scouting the route throughout the journey to avoid police detection. “The drivers were located in rest areas in Belgium before they drove the equipment to a spot at the time of departure,” said Europol.

“When used legally, such boats would not be suitable nor safe for the transportation of more than 10 individuals. However, on average, smugglers put around 50 migrants in one of these boats. In total, the investigators have gathered evidence linking at least 55 departures that were facilitated solely by this smuggling network. The suspects collected between €1,000 [£856] and €3,000 per migrant for a place,” said Europol.

In a detailed four-page statement, Europol said small-boat smuggling activities had increased on the English route since 2019 and “are becoming increasingly violent while adapting” activities and crossing points.

It said the operations were complex, with intermediaries recruiting people hoping to cross, maintaining contacts with low-level criminals, overseeing logistical arrangements and handling payments while the gang bosses are often elsewhere.

Police from Bruges and Lille were involved, with sources saying the gangs operating in the Calais region were either controlled or “have to get the blessing of” Iraqis who run the criminal operation from afar.

EU police sources say people-smuggling on the northern French coast has been dominated by Iraqi gangs for years.

The UK and the EU are about to agree a deal to share real-time data on migration in a further sign of thawing post-Brexit relations.

The deal is expected to be signed in London on Friday by Sunak and the EU home affairs commissioner, Ylva Johansson, giving the UK access to Frontex (the EU’s border agency) risk analysis and to information from Eurosur, the EU’s drone and satellite surveillance of the Mediterranean and other external border areas.

• Immigration and asylum

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## NUMBER SYSTEM

Mar 13, 2019

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NUMBER SYSTEM. Compiled by : S. Agarwal, Lecturer &amp; Systems Incharge St. Xavier’s Computer Centre, St. Xavier’s College Kolkata. March-2003. Introduction

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NUMBER SYSTEM Compiled by : S. Agarwal, Lecturer & Systems Incharge St. Xavier’s Computer Centre, St. Xavier’s College Kolkata. March-2003

Introduction A number system defines a set of values used to represent quantity. We talk about the number of people attending class, the number of modules taken per student, and also use numbers to represent grades achieved by students in tests. Quantifying values and items in relation to each other is helpful for us to make sense of our environment. We do this at an early age; figuring out if we have more toys to play with, more presents, more lollies and so on. The study of number systems is not just limited to computers. We apply numbers every day, and knowing how numbers work will give us an insight into how a computer manipulates and stores numbers.

The Romans devised a number system which could represent all the numbers from 1 to 1,000,000 using only seven symbols • I = 1 • V = 5 • X = 10 • L = 50 • C = 100 • D = 500 • M = 1000 • A small bar placed above a symbol indicates the number is multiplied by 1000.

The Decimal Number System The primary number system used is a base ten number system. Base ten number systems are called decimal number systems. In decimal we have ten numerals, 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

Counting in decimal: When we count, we start at 1 and count up to 9. The next number is 10. That is, we create a place for the tens digit and put zero in the ones position. We continue to count by adding one to the ones place until we run out of digits again at 19. Then we reset the ones place to zero and increment the tens place to get 20. We continue in this way until we reach 99. At that point we create a third digit to hold hundreds and reset the tens and ones place to zero to get 100. And so on. Each time we change a digit, all the digits to its right are set to zero. So the number after 299 is 300, with zeros to the right of the 3.

9735 = 9000 is equivalent to 9 * 1000 is equivalent to 9 * 103 + 700 7 * 100 7 * 102 + 30 3 * 10 3 * 101 + 5 5 * 1 5 * 100 So 9735 = (9 * 103) + (7 * 102) + (3 * 101) + (5 * 100).

The Octal Number System We can use a number system with only eight numerals, 0 through 7. A system with only eight numerals is called octal.

Counting in Octal In octal, instead of ten digits, we only have eight. So we resort to changing the digits to the left more frequently. Counting in base 8, we get: 0 1 2 3 4 5 6 7 10 11 12 13 14 15 16 17 20 21 22 23 24 25 26 27

octal-decimal octal-decimal octal-decimal octal-decimal octal-decimal octal-decimal octal-decimal Since the octal number 10 follows 7, 10 in octal is 8 in decimal. 11 in octal is 9 in decimal. And so on. 0 - 0 10 - 8 20 - 16 ... 70 - 56 100 - 64 ... 1 - 1 11 - 9 21 - 17 71 - 57 101 - 65 2 - 2 12 - 10 22 - 18 72 - 58 102 - 66 3 - 3 13 - 11 23 - 19 73 - 59 103 - 67 4 - 4 14 - 12 24 - 20 74 - 60 104 - 68 5 - 5 15 - 13 25 - 21 75 - 61 105 - 69 6 - 6 16 - 14 26 - 22 76 - 62 106 - 70 7 - 7 17 - 15 27 - 23 77 - 63 107 - 71

5732 = 5000 (octal) = 5 * 1000 (octal) = 5 * 83 = 5 * 512 (decimal) = 2560 (decimal) Octal Digit Positions and Values In base 8, each digit occupies a position worth eight times the position to its right, instead of ten times as in base 10. So if 5732 is an octal number, it can be read as: + 700 (octal) = 7 * 100 (octal) = 7 * 82 = 7 * 64 (decimal) = 448 (decimal) + 30 (octal) = 3 * 10 (octal) = 3 * 81 = 3 * 8 (decimal) = 24 (decimal) + 2 (octal) = 2 * 1 (octal) = 2 * 80 = 2 * 1 (decimal) = 2 (decimal) Total = 3034 (decimal) We total the decimal values of each octal digit to get the decimal equivalent. So 5732 (octal) is 3034 (decimal).

To convert a decimal number to octal, we simply repeat dividing by 8 and saving the remainder. To convert 3034 in decimal to octal, start by dividing 3034 by 8 to get 379 with a remainder of 2. The first remainder will be the last digit in the octal number; the second remainder will be the second digit from the right; and so on. That is, all we need to do is write the remainders right-to-left as we divide by 8: Step Divide Equals Remainder Digits (1) 3034 / 8 = 379 2 2 (3) 379 / 8 = 47 3 32 (5) 47 / 8 = 5 7 732 (6) 5 / 8 = 0 5 5732

The Hexadecimal Number System We can use a number system with sixteen numerals. A base 16 number system is call hexadecimal or just hex. We can use our usual 0 through 9 for the first ten digits, then use the letters A for 10, B for 11, C for 12, D for 13, E for 14 and F for 15.

Counting in Hexadecimal In hexadecimal, we count the same same way we did in decimal and octal. But instead of ten digits or eight digits, we have sixteen, 0-9, A-F. So we resort to changing the digits to the left less frequently than in decimal or octal. Counting in base 16, we get: 0 1 2 3 4 5 6 7 8 9 A B C D E F 10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F 20 21 22 23 24 25 26 27 28 29 2A 2B 2C 2D 2E 2F

hex-dec hex-dec hex-dec hex-dec hex-dec hex-dec hex-dec 0 - 0 10 - 16 20 - 32 ... F0 - 240 100 - 256 ... 1 - 1 11 - 17 21 - 33 F1 - 241 101 - 257 2 - 2 12 - 18 22 - 34 F2 - 242 102 - 258 3 - 3 13 - 19 23 - 35 F3 - 243 103 - 259 4 - 4 14 - 20 24 - 36 F4 - 244 104 - 260 5 - 5 15 - 21 25 - 37 F5 - 245 105 - 261 6 - 6 16 - 22 26 - 38 F6 - 246 106 - 262 7 - 7 17 - 23 27 - 39 F7 - 247 107 - 263 8 - 8 18 - 24 28 - 40 F8 - 248 108 - 264 9 - 9 19 - 25 29 - 41 F9 - 249 109 - 265 A - 10 1A - 26 2A - 42 FA - 250 10A - 266 B - 11 1B - 27 2B - 43 FB - 251 10B - 267 C - 12 1C - 28 2C - 44 FC - 252 10C - 268 D - 13 1D - 29 2D - 45 FD - 253 10D - 269 E - 14 1E - 30 2E - 46 FD - 253 10D - 269 F - 15 1F - 31 2F - 48 FF - 255 10F - 271 Since the hex number A follows 9, A in hex is 10 in decimal. B in hex is 11 in decimal. After F in hex (15 in decimal) we have 10 (16 in decimal). And so on.

3F72 = 3000 (hex) = 3 * 1000 (hex) = 3 * 163 = 3 * 4096 (decimal) = 12288 (decimal) Hex Digit Positions and Values In base 16, each digit occupies a position worth sixteen times the position to its right, instead of ten times as in base 10 or eight times as in octal. So if 3F72 is an hex number, it can be read as: + F00 (hex) = F * 100 (hex) = 15 * 162 = 15 * 256 (decimal) = 3840 (decimal) + 70 (hex) = 7 * 10 (hex) = 7 * 161 = 7 * 16 (decimal) = 112 (decimal) + 2 (hex) = 2 * 1 (hex) = 2 * 160 = 2 * 1 (decimal) = 2 (decimal) Total = 16242 (decimal) We total the decimal values of each hex digit to get the decimal equivalent. So 3F72 (hex) is 16242 (decimal).

Step Divide Equals Remainder Digits Converting Decimal to Hex We can convert a decimal to hex using the same procedure we used to convert decimal to octal. The only difference is that we divide by 16 each time since we are working in base 16. In the following steps we convert 16242 from decimal to hex: (1) 16242 / 16 = 1015 2 = 2 (hex) 2 (2) 1015 / 16 = 63 7 = 7 (hex) 72 (3) 63 / 16 = 3 15 = F (hex) F72 (4) 3 / 16 = 0 3 = 3 (hex) 3F72 So 16242 in decimal is written as 3F72 in hex.

The Binary Number System The base 2 number system, called binary is based on powers of 2 and contains only two digits, 0 and 1. 01001001010101110101010001010101101 10101010000000111101010101011111010

Counting in Binary • With only two numerals, 1 (one) and 0 (zero), counting in binary is pretty simple. Just keep in mind the following: • 0 + 0 = 0 • 0 + 1 = 1 • 1 + 0 = 1 • 1 + 1 = 10 • 1 + 1 + 1 = 11

We we would count in binary as follows: bin-dec bin-dec bin-dec bin-dec 0 - 0 1000 - 8 10000 - 16 11000 - 24 1 - 1 1001 - 9 10001 - 17 11001 - 25 10 - 2 1010 - 10 10010 - 18 11010 - 26 11 - 3 1011 - 11 10011 - 19 11011 - 27 100 - 4 1100 - 12 10100 - 20 11100 - 28 101 - 5 1101 - 13 10101 - 21 11101 - 29 110 - 6 1110 - 14 10110 - 22 11110 - 30 111 - 7 1111 - 15 10111 - 23 11111 - 31

Binary Digit Positions and Values In base 2, each digit occupies a position worth two times the position to its right, instead of ten times as in base 10, eight times as in octal, or 16 as in hex. So if 1101001 is a binary number, it can be read as:

1101001 = 1000000 (bin) = 1 * 26 = 1 * 64 (decimal) = 64 (decimal) + 100000 (bin) = 1 * 25 = 1 * 32 (decimal) = 32 (decimal) + 00000 (bin) = 0 * 24 = 0 * 16 (decimal) = 0 (decimal) + 1000 (bin) = 1 * 23 = 1 * 8 (decimal) = 8 (decimal) + 000 (bin) = 0 * 22 = 0 * 4 (decimal) = 0 (decimal) + 00 (bin) = 0 * 21 = 0 * 2 (decimal) = 0 (decimal) + 1 (bin) = 1 * 20 = 1 * 1 (decimal) = 1 (decimal) TOTAL = 105 (decimal) We total the decimal values of each binary digit to get the decimal equivalent. So 1101001 (binary) is 105 (decimal).

Converting Decimal to Binary We can convert a decimal to binary by dividing by 2 each time since we are working in base 2. In the following steps we convert 105 from decimal to binary: Step Divide Equals Remainder Digits (1) 105 / 2 = 52 1 1 (2) 52 / 2 = 26 0 01 (3) 26 / 2 = 13 0 001 (4) 13 / 2 = 6 1 1001 (5) 6 / 2 = 3 0 01001 (6) 3 / 2 = 1 1 101001 (7) 1 / 2 = 0 1 1101001 So 105 in decimal is written as 1101001 in binary.

Converting Between Hex, Octal and Binary bin-octal-dec bin-octal-dec bin-octal-dec bin-octal-dec 0 - 0 - 0 1000 - 10 - 8 10000 - 20 - 16 11000 - 30 - 24 1 - 1 - 1 1001 - 11 - 9 10001 - 21 - 17 11001 - 31 - 25 10 - 2 - 2 1010 - 12 - 10 10010 - 22 - 18 11010 - 32 - 26 11 - 3 - 3 1011 - 13 - 11 10011 - 23 - 19 11011 - 33 - 27 100 - 4 - 4 1100 - 14 - 12 10100 - 24 - 20 11100 - 34 - 28 101 - 5 - 5 1101 - 15 - 13 10101 - 25 - 21 11101 - 35 - 29 110 - 6 - 6 1110 - 16 - 14 10110 - 26 - 22 11110 - 36 - 30 111 - 7 - 7 1111 - 17 - 15 10111 - 27 - 23 11111 - 37 - 31 Converting between binary, octal and hex is simple. Binary is base 2. Octal is base 8, and 8 is 23. That is, it takes exactly three binary digits to make one octal digit. If we line up the binary numbers and octal numbers, the connection is even more obvious:

What this means is that we can convert from binary to octal simply by taking the binary digits in groups of three and converting. Consider the binary number 10110100111100101101001011. If we take the digits in groups of three from right to left and convert, we get: 10110100111100101101001011 2 64745513 That is, 10110100111100101101001011 (binary) is 264745513 (octal).

Converting from octal to binary is just as easy. Since each octal digit can be expressed in exactly three binary digits, all we have to do is convert each octal digit to three binary digits. Converting 7563021 in octal to binary goes as follows: 7 5 6 3 0 2 1 111 101 110 011 000 010 001 So 7563021 (octal) is 111101110011000010001 (binary.)

Since (almost!) all computers have a binary architecture, octal is very useful to programmers. For humans, octal is more concise, smaller, easier to work with, and less prone to errors than binary. And since it is so easy to convert between binary and octal, octal is a favored number system for programmers.

In the same way, hex is base 16 and 16 is 24. That is, it takes exactly four binary digits to make a hex digit. By taking binary digits in groups of four (right to left) we can convert binary to hex. Consider once more the binary number 10110100111100101101001011. By grouping in fours and converting, we get: 10 1101 0011 1100 1011 0100 1011 2 D 3 C B 8 B So 10110100111100101101001011 (binary) is the same number as 2D3CB8B (hex), and the same number as 264745513 (octal).

Converting from hex to binary, simply write each hex digit as four binary digits. In this way we can convert 6F037C2: 6 F 0 3 7 C 2 0110 1111 0000 0011 0111 1100 0010 Since we can drop the leading zero, 6F037C2 (hex) is 110111100000011011111000010 (binary).

These days, octal tends to be used by programmers who come from a mini-computer background or who work with unicode. Hex tends to be preferred by programmers with a mainframe background or who work with colors. Many programmers are at home with either.

nibbleIn computers and digital technology, a nibble is four binary digits or half of an eight-bit byte. Maximum number in a nibble : 1111 = 15 A nibble can be conveniently represented by one hexadecimal digit.

BCD Binary-coded decimal, or BCD, is a method of using binary digits to represent the decimal digits 0 through 9. A decimal digit is represented by four binary digits, as shown below: The binary combinations 1010 to 1111 are invalid and are not used.

UNPACKED & PACKED BCD In unpacked BCD, a decimal digit is stored in one byte and in packed BCD, four bits are used to keep one digit, so two digits are stored in one byte, one in the lower half and one in the upper half of the byte. BCD and binary are not the same. For example, 4910 in binary is 1100012, but 4910 in BCD is 01001001BCD. 4 9 01001001 = 01001001BCD (PACKED BCD) Each decimal digit is converted to its binary equivalent.

BCD Conversion Conversion of decimal to BCD or BCD to decimal is similar to the conversion of hexadecimal to binary and vice versa. For example, let's go through the conversion of 26410to BCD. We'll use the block format that you used in earlier conversions. First, write out the decimal number to be converted; then, below each digit write the BCD equivalent of that digit: The BCD equivalent of 26410 is 001001100100BCD

To convert from BCD to decimal, simply reverse the process as shown: The DECIMAL equivalent of 100110000011BCD is 98310

ASCII Code ASCII, pronounced "ask-key", is the common code for microcomputer equipment. The standard ASCII character set consists of 128 decimal numbers ranging from zero through 127 assigned to letters, numbers, punctuation marks, and the most common special characters. The Extended ASCII Character Set also consists of 128 decimal numbers and ranges from 128 through 255 representing additional special, mathematical, graphic, and foreign characters.

The Standard ASCII character set is divided into four groups of 32 characters. The first 32 characters, form a special set of non-printing characters called the control characters. We call them control characters because they perform various printer/display control operations rather than displaying symbols.

Examples of common control characters include: • carriage return which positions the cursor to the left side of the current line of characters, • line feed which moves the cursor down one line on the output device • back space which moves the cursor back one position to the left • Unfortunately, different control characters perform different operations on different output devices. There is very little standardization among output devices. To find out exactly how a control character affects a particular device, you will need to consult its manual.

The second group of 32 ASCII character codes comprise various punctuation symbols, special characters, and the numeric digits. The most notable characters in this group include the: • space character • numeric digits 0 through 9 • Note that the numeric digits differ from their numeric values only in the high order nibble. By subtracting 30h from the ASCII code for any particular digit you can obtain the numeric equivalent of that digit.

The third group of 32 ASCII characters is reserved for the upper case alphabetic characters. The ASCII codes for the characters "A" through "Z" lie in the range 41h through 5Ah. Since there are only 26 different alphabetic characters, the remaining six codes hold various special symbols. The fourth, and final, group of 32 ASCII character codes are reserved for the lower case alphabetic symbols, five additional special symbols, and another control character (delete).

ISCII Indian Script Code for Information Interchange The  ISCII code table is a super-set of all  the  characters required  in  the ten Brahmi-based Indian  scripts.   An  optimal keyboard  overlay  for  these scripts is  made  possible  by  the phonetic nature of the alphabet.  The differences between scripts primarily are in their written forms, where different combination rules get used.

The 8-bit ISCII code retains the standard ASCII code,  while the  Indian script keyboard overlay is designed for the  standard English  can  co-exist with Indian scripts.  This  approach  also makes  it  feasible  to use Indian scripts  along  with  existing English computers and software, so long as 8-bit character  codes are allowed.

The common INSCRIPT keyboard overlay allows typing  of  all the  ten  Indian  scripts.  This overlays fits  on  any  existing English  keyboard.  Alternating between the English and  Inscript overlay is achieved through the CAPSLOCK key. The  INSCRIPT  keyboard, provides a  logical  and  intuitive arrangement  of vowels and consonants.  It is based both  on  the phonetic  properties  and the relative usage frequencies  of  the letters.   Not  only does this made the keyboard much  easier  to learn, but also enables a person to type subsequently in all  the Indian scripts.

EBCDIC Extended Binary Coded Decimal Interchange Code It is an 8 bit character encoding used on IBM mainframes and AS/400s. It is descended from punched cards and the corresponding six bit Binary Coded Decimal Code that most of IBM's computer peripherals of the late 1950s and early 1960s used. Outside of such IBM systems, ASCII are normally used instead; EBCDIC is generally considered an anachronism. EBCDIC takes up eight bits, which are divided in two pieces. The first four bits are called the zone and represent the category of the character, whereas the last four bits are the called the digit and identify the specific character. There are a number of different versions of EBCDIC, customised for different countries.

BINARY ARITHMETIC

1 1 1 1 0 0 0 0 0 0 1 1 1 0 1 0 1 0 1 0 0 1 0 1 1 1 0 0 1 1 0 0 --- --- --- --- --- --- --- --- --- --- --- --- 0 01 01 10 11 10 10 01 10 01 01 00 The Binary Addition Algorithm To add two 1-bit (representations of) integers: Count the number of ones in a column and write the result in binary. The right bit of the result is placed under the column of bits. The left bit is called the "carry out of the column".

A A B B CarryDigit C CARRY UnitDigit UNIT 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1 0 0 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1

Signed Binary Integers We will not be using a minus sign (-) to represent negative numbers. We would like to represent our binary numbers with only two symbols, 0 and 1. There are a few ways to represent negative binary numbers. The simplest of these methods is called ones complement, where the sign of a binary number is changed by simply toggling each bit (0's become 1's and vice-versa). This has some difficulties, among them the fact that zero can be represented in two different ways (for an eight bit number these would be 0000 0000 and 1111 1111)., we will use a method called two's complement notation which avoids the pitfalls of one's complement.

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Download ppt "Number System." Introduction A set of values used to represent different quantities For example, a number student can be used to represent the number of students in the class Digital computer represent all kinds of data and information in binary numbers Includes audio, graphics, video, text and numbers Total number of digits used ...

18. PDF Inventing Your Own Number System

determining the number represented. Tally marks are a simple system, but representing large numbers requires many strokes. In our number system, symbols for digits and the positions they are located combine to represent the value of the number. It is possible to create a system where symbols stand for operations rather than values. For

19. Basic of number system

2. A number system can be used to represent the number of students in a class or number of viewers watching a certain TV program etc. The digital computer represents all kinds of data and information in binary numbers. It includes audio, graphics, video, text and numbers. The total number of digits used in a number system is called its b...

20. PPT

Presentation 1 / 225 Download Presentation >> 7th Grade Math Number System Apr 03, 2019 3.64k likes | 5.23k Views 7th Grade Math Number System. Number System Unit Topics. Click on the topic to go to that section. Number System, Opposites & Absolute Value. Comparing and Ordering Rational Numbers. Adding Rational Numbers.

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When a user's cell phone isn't connected to a cellular network, they will typically alert the user by giving an indication in the phone's status bar. Those notifications usually say "No ...

22. OpenAI Unveils Generative AI Video System, Sora, to Limited Number of

OpenAI teased a new artificial intelligence system that can create realistic-looking videos based on text prompts from users, making it the latest AI company to embrace generative video technology ...

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Closer to 7 a.m. ET, more than 19,500 Verizon users and over 850 T-Mobile users reported outages. As of 7:29 a.m. ET, over 60,000 AT&T customers were reporting outages, while nearly 12,000 Cricket ...

24. CBP Releases January 2024 Monthly Update

Tue, 02/13/2024. WASHINGTON — U.S. Customs and Border Protection (CBP) released operational statistics today for January 2024. Migrant encounters along the southwest border were significantly lower than experienced in December. CBP monthly reporting can be viewed on CBP's Stats and Summaries webpage. "As a result of seasonal trends, as ...

25. PPT

Presentation Transcript. Computer Number Systems ACSL. All computers - from large mainframes to hand-held micros - ultimately can do one thing: detect whether an electrical signal is "on" or "off". • Computer programs in any language are converted by various pieces of systems software into sequences of bits (Binary digITs) which ...

26. Number System in CoMpUtEr

Octal Number System Characteristics of octal number system are as follows: Uses eight digits, 0,1,2,3,4,5,6,7. Also called base 8 number system Each position in an octal number represents a 0 power of the base (8). Example 80 Last position in an octal number represents a x power of the base (8). Example 8x where x represents the last position - 1.

27. Calais people-smuggling gang broken up with 19 arrests, says Europol

Thu 22 Feb 2024 06.30 EST. One of the most active and largest people-smuggling gangs operating in Calais has been dismantled with 19 "high-value targets" arrested by German, French and Belgian ...

28. PPT

The Romans devised a number system which could represent all the numbers from 1 to 1,000,000 using only seven symbols • I = 1 • V = 5 • X = 10 • L = 50 • C = 100 • D = 500 • M = 1000 • A small bar placed above a symbol indicates the number is multiplied by 1000. The Decimal Number System The primary number system used is a base ten number system.