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COMPUTER SYSTEM 2.2 NUMBER SYSTEM AND REPRESENTATION (CONVERSION OF…
COMPUTER SYSTEM
2.2 NUMBER SYSTEM AND REPRESENTATION
NUMBER SYSTEM
Decimal Numbers (base 10)
Binary Numbers (base 2)
Hexadecimal Numbers (base 16)
BINARY NUMBERS
Uses 2 digits; 0
and 1.
Binary numbers are formed by combining
digits 0 and 1.
Examples of binary numbers:
– 110, 0010, 1110, 10000111
DECIMAL NUMBERS
uses 10 digits;
0,1,2,3,4,5,6,7,8,9.
Formed by combining
any digits from 0 to 9.
Examples of decimal numbers:
– 18, 265, 2016, 15000000
HEXADECIMAL NUMBERS
Uses 16 symbols;
0,1,2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F.
Digits 0 to 9 represents values 0 to 9, while
alphabet A to F represents values 10 to 15.
Hexadecimal numbers are formed by
combining any symbols from 0 to F.
Examples of hexadecimal numbers:
– 25, A1, D6, 95C4
CONVERSION OF NUMBERS
DECIMAL TO BINARY
BINARY TO DECIMAL
Convert the binary number 10110 to decimal number.
Solution:
01102
= (1 x 24) + (0 x 23) + (1x 22 ) + (1 x 21) + (0 x 20)
= 16 + 0 + 4 + 2 + 0
= 2210
DECIMAL TO HEXADECIMAL
HEXADECIMAL TO DECIMAL
SOLUTION :
BA8
= (B x162)+ (A x161) + (8 x160)
= (11x256) + (10x16) + (8x1)
= 2816 + 160 + 8
= 298410
BINARY TO HEXADECIMAL
HEXADECIMAL TO BINARY
