BASED TO DECIMAL SYSTEM Archives

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 Also See: Area Length