03/05/2023

COMPUTER NUMBER SYSTEM

D E F I N I T I O N , B A S E / R A D I X O F D E C I M A L , B I N A R Y, O C T A L , H E X A - D E C I M A L .

SAPNA ARORA SAINI

03/05/2023 SAPNA ARORA SAINI

INTRODUCTION• A number is a mathematical object used to count, measure, and label.• Every computer stores the information

in the form of letters, numbers, other

special characters and etc in coded forms.

In computers commonly we used

number systems.

Number systems are of two types • Non Positional • Positional

03/05/2023 SAPNA ARORA SAINI

POSITIONAL VERSUS NON POSITIONAL NUMBER SYSTEM

Non Positional Number System• In Non positional number system

Each symbol represents the same value regardless of its position in a number and to find the value of a number one has to count the number of the symbols present in the number, we have symbols such as I for 1, II for 2, III for 3 and etc.•  

Positional Number System• In positional number system symbols represent

different values depending upon the position they occupy in a number. The value of each digit in a number is determined by three considerations

• Digit itself

• Position of the digit in number

• Base of number system (i.e. base means total number of digits in the number system)

• We use decimal number system in our daily life. In this system base is 10 because there are 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) in this number system

03/05/2023 SAPNA ARORA SAINI

RADIX/BASE OF A NUMBER SYSTEM• In NUMBER SYSTEM, The radix or base is the number of unique digits, including zero, used to

represent numbers in apositional numeral system.

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TYP ES O F PO SITI O NAL

NUM BER S YS TEM S•DECIMAL NUMBER SYSTEMWe use decimal number system in our daily life. In this system base is 10 because it contains 10 digits which are as 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. • 2586 is written as in decimal number system = 258610

• 25.86 is written as in decimal number system = 25.8610

Decimal number system

Binary number system

Octal number system

Hexadecimal number system

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POSITIONING IN DECIMAL NUMBER SYSTEM

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BINARY NUMBER SYSTEM

• Digital computers use digital signals which can only be 'on' or 'off'. To do something useful with this, it is necessary to find a system that only deal with 'on' and 'off'. The answer is binary which uses only '1' and '0'. Now meaning of '1' is 'on' and '0' is 'off'.• Each and every computer machine uses the binary number system. The base of

binary number system is 2 because it contains only two digits which are 0 and 1.

03/05/2023 SAPNA ARORA SAINI

03/05/2023 SAPNA ARORA SAINI

OCTAL NUMBER SYSTEMThe base of octal number system is 8 because this number system consists of eight digits starting from 0 to 7. For example 272, 103, 145 etc

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HEXADECIMAL NUMBERSYSTEMThe base of hexadecimal number system is 16

because

it includes 16 digits – 0 – 9, A, B, C, D, E, F

where (A is for 10, B is for 11, C – 12, D – 13,

E – 14, F – 15).

For example: 3FA, 87B, 113, etc.

03/05/2023 SAPNA ARORA SAINI

03/05/2023 SAPNA ARORA SAINI