Answer to Question #335274 in Combinatorics | Number Theory for Maneo

Question

Subtract the given numbers using the indicated complements. Also show your answers in non-complement form, using (+) and (-) to indicate the sign of the number.

a. 848₁₀ – 692₁₀ in 10’s complement

b. 618₁₆ – 8E3₁₆ in 16’s complement

c. 10001100₂ – 11100011₂ in 2’s complement

d. 11000101₂ – 10001110₂ in 1’s complement

e. 4020₈ – 2021₈ in 8’s complement 

Answer 1

a. Complement for 692 is 308

(10-2=8, 9-9=0, 9-6=3). For the first and second number we use complement -1 value.

Then 848+308=1156. And remove the first number. Answer is 156.

b. Complement for 618.

At first we should find 15' s compliment to 618. It is (15-8=7, 15-1=14=E,15-6=9) 9E7, then we should add 1 to the last number. So 16's complement is 9E8

Then 8E3+9E8=12CB

And remove the first number. Answer: 2CB

c. (-11100011) equals 00011101. Then we sum it with 10001100 bit for a bit starting from the last. If the sum is greater 1, then we write 0 and add 1 at the next bit. It equals 10101001.

d.(-10001110) equals

01110001. The sum it with 11000101 bit for a bit starting from the last. If the sum is greater 1, then we write 0 and add 1 at the next bit.equal 100110110

e. At first we should find 7' complement to 2021. It is (7-1=6, 7-2=5, 7-0=7,7-2=5) 5756 and then add 1. 5757.

Then 4020+5757=A777