NUMBER BASES
CONVERSION OF OTHER BASED TO DECIMAL SYSTEM
To convert numbers in other bases to denary system, expand the given number in powers of its base and evaluate.
Examples
1) Convert the following numbers to base ten
(i) 10012 (ii) 255eight (iii) 35416
(i) 10012 = 1 x 23 + 0 x 22 + 0 x 21 + 1 x 20
= 1 x 8 + 0 x 4 + 0 x 2 + 1 x 1
= 8 + 0 + 0 + 1
= 9ten
(ii) 255eight = 2 x 82 + 5 x 81 + 5 x 80
= 2 x 64 + 5 x 8 + 5 x 1
= 128 + 40 + 5
= 173ten
(iii) 35416 = 3 x 162 + 5 x 161 + 4 x 160
= 3 x 256 + 5 x 16 + 4 x 1
= 768 + 80 + 4
= 852ten
CHANGING FROM BINARY TO OCTAL AND HEXADECIMAL
To convert from a number system to another one (not denary), it is usual to convert to base ten and then convert the base ten number to the new base number.
However, binary numbers can be converted to octal and hexadecimal numbers because of the fact that 23 = 8 and 22 = 16.
Examples
(1) Convert 110110two to base 8, base 16
(note 23 = 8 and 24 = 16)
(i) 1101102 = (1102) (1102)
= 66eight (1102 = 6ten)
(ii) 1101102 = (00112) (01102)
= 36hex (00112 = 3ten)
2) Convert 1110110two to base 16
1110110 = (01110110)two
= 7616
3) Convert 1000101two to base eight
1000101two = (001)(000)(101)
= 103eight
4) Convert 62eight to base two
62eight = 6 2
110 010
= 110010two
5) Change A0316 = A 0 3
1010 0000 0011
= 10100000011two
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