Answer to Question #335272 in Combinatorics | Number Theory for Maneo

Question

Subtract the following numbers in the indicated bases (do not make any conversion to a different base):

a. 4607₈ - 1705₈

b. F32₁₆ - A65₁₆ 

c. 110010₂ - 010101₂

d. 1234₅ - 432₅ 

Answer 1

Complement (7's) to the 1705 is 6072 (7-5=2, 7-0=7, 7-7=0,7-1=6)

Then 8' s complement to 1705 is 6072+1=6073.

Then 6073+ 4607=12702

The first bit is not used, so

Answer: 2702

b. Complement 15's to the A65 is (15-5=10=A, 15-6=9, 15-10=5) 59A.

Then 16's complement is 59A+1=59B

Then 59B+F32=14CD

The first bit is not used, so

Answer: 4CD

c.(-010101)=101010+1=101011

Then 110010+101011=1011101

The first bit is not used, so

Answer: 011101

d. Complement (4's) to the 432 is (4-2=2, 4-3=1,4-4=0) 012.

Then 5's complement is 012+1=013

Then 013+1234=1302. The first bit is not used, so

Answer: 302