GATE EC 2020 Set 1 — Question 48
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Digital Circuits → Number Representations → 1's & 2's Complement
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Question
, , and are the decimal integers corresponding to the 4-bit binary number considered in signed magnitude, 1's complement, and 2's complement representations, respectively. The 6-bit 2's complement representation of is
Correct answer
(A) 110101
Solution
Given 4-bit binary number is .
1.Signed Magnitude (): MSB is 1 (negative), magnitude is . So, .
2.1's Complement (): MSB is 1 (negative). Magnitude is found by complementing the remaining bits: . So, .
3.2's Complement (): MSB is 1 (negative). Magnitude is found by taking the 2's complement of , which is . So, .
Sum .To find the 6-bit 2's complement of :- in 6-bit binary:
- 1's complement:
- 2's complement:
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