Which of the following is the result of (-13)₅ + (34)₅, when it is performed…
2022
Which of the following is the result of (-13)₅ + (34)₅, when it is performed using 5's complement?
- A.
(-11)₁₀
- B.
(21)₅
- C.
(21)₁₀
- D.
(21)₉
Attempted by 67 students.
Show answer & explanation
Correct answer: B
First, interpret the values in decimal: (-13)₅ is -8₁₀ and (34)₅ is 19₁₀.
To find the 5's complement of -13₅, invert digits (4-1=3, 4-3=1) to get 31₅, then add 1 for 32₅.
Add 32₅ and 34₅ to get 121₅. Discard the end-around carry, leaving 21₅ as the final result.
Verification: -8 + 19 = 11₁₀, which converts back to (21)₅.