DECIMAL NUMBER SYSTEM AND

BYNARY SYSTEM

Binary Representation

• The basis of all digital data is binary representation.

• Binary - means ‘two’– 1, 0– True, False– Hot, Cold– On, Off

BASE 10, BASE 2

953.7810 = 9 x 102 + 5 x 101 + 3 x 100 + 7 x 10-1 + 8 x 10-2 =

= 900 + 50 + 3 + 0.7 + 0.08 = 953.78

1001.112 = 1 x 23 + 0 x 22 + 1 x 21 + 1 x 20 + 1 x 2-1 + 1 x 2-2 =

= 8 + 0 + 2 + 1 + 0.5 + 0.25 = = 11.75

Conversion of Decimal Integer To ANY BaseExample

Convert 53 to binary

53/2 = 26, rem = 126/2 = 13, rem = 013/2 = 6 , rem = 16 /2 = 3, rem = 03/2 = 1, rem = 11/2 = 0, rem = 1

5310 = 1101012

= 1x25 + 1x24 + 0x23 + 1x22 + 0x21 + 1x20

= 32 + 16 + 0 + 4 + 0 + 1 = 53