MadeEasy Full Length Test 2018: Digital Logic - Number Representations

Question

2’s complement representation of the number $(-89)_{10}$ is

• A. 7
• B. 5
• C. 4
• D. 3

I don’t understand their solution. Please help.

Comments

in question they have asked for 2's complement in solution they have solved for sum of bits..? ambiguity?

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I'm not getting the question correctly.But some of the case i can give.

1.Number of bits to represent.

$-2^{n-1} \geq -89 $

$2^{n-1} \geq 2^{7} $

n = 8 bits.

2.2's complement of the -89.

10100111 .

Sum of bits = 1 + 0 + 1 + 0 +0+ 1+1+1 => 5.

Number of bits = 8.

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@arvin,@kumar.dilip

Exactly. I am also not getting it. And it said 2's complement representation of -89 and not 2's complement of -89.

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@MiNiPanda i think there is some fault in the question!