Convert the following numbers in the given bases into their equivalents in the desired bases: A. (110.101)_2 = (?)_10 B. (1318)_10 = (?)_8

GATE 1993 · Digital Logic · Number Representation · medium

Answer: A. (110.101)_2 = (6.625)_10 B. (1318)_10 = (2446)_8

1. Convert (110.101)_2 to decimal: Integer part: 1*4 + 1*2 + 0*1 = 6. Fractional part: 1*(1/2) + 0*(1/4) + 1*(1/8) = 0.5 + 0 + 0.125 = 0.625. Total = 6 + 0.625 = 6.625.
2. Convert (1318)_10 to octal by repeated division: 1318 / 8 = 164 remainder 6 164 / 8 = 20 remainder 4 20 / 8 = 2 remainder 4 2 / 8 = 0 remainder 2 Reading remainders bottom-up: 2, 4, 4, 6 => (2446)_8. Verification: 2*512 + 4*64 + 4*8 + 6 = 1024 + 256 + 32 + 6 = 1318. Correct.