What decimal no. is represented by the binary number 111.111 ? 1 1 1 . 1 1 1 4 2 1 0.5 0.25 0.125 1 x 0.125 = 0.125 1 x 0.25 = 0.25 1 x 0.5 = 0.5 1 x 1 = 1 1 x 2 = 2 1 x 4 = 4 + ------- 7.875 What decimal no. is represented by the binary number 1111111 ? Binary Decimal 1 = 1 10 = 2 100 = 4 1000 = 8 10000= 16 100000= 32 1000000= 64 10000000= 128 1111111 = 127 1+ ------- 10000000 We did (2^7) - 1 2^7= 128 128-1 = 127 ------ 00 01 10 11 3 100 (4-1) ----- 000 001 010 011 100 101 110 111 1000 = (8-1)= 7 ----- What decimal no. is represented by the octal no. 123.7 ? 1 2 3 . 7 64 8 1 1/8 7 x 1/8 = 7 * 0.125 = 0.875 3 x 1 = 3 2 x 8 = 16 1 x 64 = 64 + -------- 83.875 --- What decimal no. is represented by the hexadecimal no.? A10.4 ? A 1 0 . 4 256 16 1 1/16 4 x 1/16 = 4 * 0.0625 = 0.25 0 x 1 = 0 1 x 16 = 16 A(10) x 256 = 2560 + -------- 2576.25 Base 7 ------ 100 (base 7) = 49 1 0 0 49 7 1 Question -------- Convert the decimal no. 128.75 to binary? 128 - divide by 2 repeatedly. Gather your remainders 128 / 2 = 64 r 0 64 /2 = 32 r 0 32 /2 = 16 r 0 16 /2 = 8 r 0 8 /2 = 4 r 0 4 /2 = 2 r 0 2 /2 = 1 r 0 1 /2 = 0 r 1 (up) 10000000 .75 x 2 = (1).5 (down) .5 x 2 = (1).0 0 10000000.11 ------ .75 x 2 = (1) .5 .5 x 2 = (1) .0 .0 ------ .625 x 2 = (1) .25 (read down) .25 x 2 = (0) .5 .5 x 2 = (1) .0 .0 Decimal= Binary .625 = .101 0.625 = 0.101 ------ Convert 8.125 (decimal) to binary. 8/2 = 4 r 0 4/2 = 2 r 0 2/2 = 1 r 0 1/2 = 0 r 1 (read up) 1000 .125 x 2 = (0) .25 (read down for fractional part) .25 x 2 = (0) .5 .5 x 2 = (1) .0 .0 (0)(0)(1) Decimal Binary 8.125 = 1000.001