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CONVERSION OF OTHER BASES TO DENARY SYSTEM Conversion of other bases to denary system. To convert numbers in the other bases to denary system, expand the given number in power of its bases. Examples: Convert 35416 to denary 35416 3 x 162 + 5 X 161 + 4 x 160 3 x 256 + 5 x 16 + 4 x 1 768 + 80 + 4 852ten Convert 255eight to base ten 2558 2 x 82 + 5 x 81 + 5 x 80 2 x 64 + 5 x 8 + 5 x 1 128 + 40 + 5 173ten Convert 10110012 to base ten 1011001two 1 x 26 + 0 x 25 + 1 x 24 + 1 x 23 + 0 x 22 + 0 x 21 + 1 x 20 1 x 64 + 0 x 32 + 1 x 16 + 1 x 8 + 0 X 4 + 0 x 2 + 1 x 1 64 + 0 + 16 + 8 + 0 + 0 +1 89ten Convert 3A716 to base ten 3A716 3 x 162 + 10 x 161 + 7 x 160 3 x 256 + 10 x 16 + 7 x 1 768 + 160 + 7 935ten ADDITION, SUBTRACTION AND MULTIPLICATION OF BINARY NUMBERS There are four rule guiding binary addition 0 + 0 0 0 + 1 1 (Always remember you are working with binary digit not decimal) 1 + 0 1 1 + 1 10 Add 1012 + 10002 Add 10011012 + 1110012 1012 + 10002 11012 10011012 + 1110012 100001102 Binary Subtraction 0 – 0 0; 0 – 1 1; 1 – 0 1; 1 – 1 0 (1). Subtract 1012 from 10012 (2). 100012 – 11112 10012 - 1012 1002 10001 - 1111 00102 Binary Multiplication The rules for binary multiplication are: 0 x0 0; 1 x 0 0; 0 x 1 0; 1 x 1 1 (1).11012 x 1102 (2). 1012 x 102 11012 x 1102 00002 + 11012 11012 10011102 1012 x 102 0002 + 1012 10102 Decimal Binary Octal Hexadecimal 0 0000 0 0 1 0001 1 1 2 0010 2 2 3 0011 3 3 4 0100 4 4 5 0101 5 5 6 0110 6 6 7 0111 7 7 8 1000 10 8 9 1001 11 9 10 1010 12 A 11 1011 13 B 12 1100 14 C 13 1101 15 D 14 1110 16 E 15 1111 17 F EVALUATION Define number base Convert the following to base 10 10011two 317eight Evaluate the following: 1012 x 1012 1110012 + 10012 101112 – 1002 See also BASIC COMPUTER CONCEPT APPLICATION SOFTWARE ART OF INFORMATION PROCESSING COMPUTER HARDWARE DATA AND INFORMATION

CONVERSION OF OTHER BASES TO DENARY SYSTEM

NUMBER BASES