.Numbering Systems: Each number system has a base also called a Radix .A decimal number system is a .system of base 10; binary is a system of base 2; octal is a system of base 8; and . hexadecimal is a system of base 16

Numbering Systems Symbols used Number System Binary Octal Base 2 8 10 16 0,1 0,1,2,3,4,5,6,7 0,1,2,3,4,5,6,7,8,9 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F where A = 10; B = 11; C = 12; D = 13; E- 14; F 15 Hexadecimal

.Converting a number .Binary to Decimal Method to convert Binary to Decimal: -1. Start at the rightmost bit -2. Take that bit and multiply by 2n where n is the current position beginning at o and increasing by 1 each time. This represents a power of two 3. Sum each terms of product until all bits have been used.

.Converting a number .Binary to Decimal .Example Convert the Binary number 101011 to its Decimal equivalent. 1 25 +0 24 + 1 23+ 0 22+ 1* 21 + 1 20 -32 0+ 8 + 0 +2 1 (43)10

.Converting a number .Binary to Decimal .Example Convert the Binary number 1001 to its Decimal equivalent. 1 23+ 0 22 +0 21 1 20

.Converting a number .Binary to Decimal . Example .Convert (11011.101)2 to decimal 24 23 22 21 20 2-1 2-2 2-3 (1 x 24)+(1x 23)+ (0 x 22)+ (1x 21)+ (1 x 20)+(1x 2-1)+ (0 x 2-2)+ (1 x 2-3) - 16+8+0+2+1+0.5+0+0.125 - (27.625)10

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