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Presentation on

Number System

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Types of Number System

Non-Positional number system Positional number system

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Non-Positional Number System Symbol represents the value regardless of its

position. Difficult to perform arithmetic operation. For example:-

I, II, III, IV, V, VI, VII, VIII, IX, X XI,XII, XIII, XIV, XV, XVI, XVII,

XVIII, XIX, XX

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Positional Number System Symbols represent different values

depending upon the position. The values of each digit is determined by:-

- Digit itself

- Position of the digit

- Base of the number system

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Decimal number The base is equal to 10 Uses 10 different symbols.

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Continue…

For example:

(2*1000) + (5*100) + (8*10) + (6*1)

=2000 + 500 + 80 + 6

=2586

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Bit Binary digit 0 or 1 Smallest possible unit of data Work with a group of bits.

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Byte Group of eight bits Used to represent one character

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Binary Number System

The base is 2. Each position represents a power of the base 2. For example:-Conversion from 00111101 to

decimal is-

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Octal Number System

The base is 8 Largest single digit is

7 For example:- decimal

equivalent to the octal number 421 is 273

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Hexadecimal Number System The base is 16 Combination of 0-9

and A-F For example:-Decimal

equivalent to the hexadecimal number 1421 is 1057

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Decimal, binary and hexadecimal representations

Decimal Binary Hexadecimal Decimal Binary Hexadecimal

1 1 1 13 1101 D

2 10 2 14 1110 E

3 11 3 15 1111 F

4 100 4 16 1 0000 10

5 101 5 17 1 0001 11

6 110 6 18 1 0010 12

7 111 7 19 1 0011 13

8 1000 8 20 1 0100 14

9 1001 9 21 1 0101 15

10 1010 A 22 1 0110 16

11 1011 B 23 1 0111 17

12 1100 C 24 1 1000 18

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Conversion of decimal representation to binary

Determine the binary equivalent of 3610

2 36

2 18

2 9

2 4

2 2

2 1

0

Remainder

0

0

1

0

0

1

Least Significant Bit (LSB)

Most significant Bit (MSB)

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Taking remainders in reverse order, we have 100100

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24 23 22 21 20 16 8 4 2 1

1 1 0 1 0 1*16

+1*8 +0*4 +1*2

+0*1

= 16 + 8 + 0 + 2 + 0= 26

Conversion of binary representation to decimal

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Conversion of hexadecimal to binary

Each hexadecimal digit is equivalent to 4 binary digits. For example:-binary equivalent to 2C :-

2 C

= 0010 1100

2C = 001011002(in binary)

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Conversion binary to hexadecimal The binary digits are arranged in groups of 4 starting

from the right. For example:-Convert 0011 0100 0110 to

hexadecimal

0011 0100 0110

3 4 6(001101000110) 2 = (346 )16

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Conversion of decimal representation to hexadecimal

(5112)10

16 5112

16 319

16 19

16 1

0

Remainder

8 = 8

15=F

3=3

1=1

Least significant bit (LSB)

Most significant bit (MSB)

(5112)10=(13F8)16

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163 162 161 160

4096 256 16 1

B 6 E

11*256

+ 6*16

+14*1

= 2816 + 96 + 14 = (2926) 10

Conversion of hexadecimal representation to decimal

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Conversion of octal representation to hexadecimal

Convert each octal digit to 3-bit binary form

Combine all the 3 bits binary form Divide the binary numbers into the 4-bit

binary form Convert these 4 bits blocks into their

respective hexadecimal symbols

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Continue…

Example (2327)8

Octal Number 2 3 2 7Binary Coded value 010 011 010 111

Combining 3-bit blocks we have 010011010111

Dividing of binary numbers into 4-bit binary blocks and converting these blocks into their respective hexadecimal symbols,

we have: 0100 1101 0111 4 D 7

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Conclusion

Same procedure to convert decimal numbers to binary, octal & hexadecimal

Same procedure to convert from binary, octal & hexadecimal to decimal numbers