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NIMCET 2024 Computer PYQ — Let the given number 11001, 1001 and 111001 be correspond to the … | Mathem Solvex | Mathem Solvex

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NIMCET 2024 — Computer PYQ

NIMCET | Computer | 2024

Let the given number 11001, 1001 and 111001 be correspond to the 2’s complement representation. Then with which one of the following decimal number, the given numbers match

Choose the correct answer:

A.
-6, -6 and -6, respectively
B.
-7, -7 and -7 respectively
(Correct Answer)
C.
-25, -9 and -57 respectively
D.
25, 9 and 57, respectively

Correct Answer:

-7, -7 and -7 respectively

Explanation

1. For $1001$ ( $4$ bits):

MSB is $1$ (Negative).
Invert bits: $0110$
Add $1$ : $0110 + 1 = 0111$
Decimal value: $-(4 + 2 + 1) = -7$

2. For $11001$ ( $5$ bits):

MSB is $1$ (Negative).
Invert bits: $00110$
Add $1$ : $00110 + 1 = 00111$
Decimal value: $-(4 + 2 + 1) = -7$

3. For $111001$ ( $6$ bits):

MSB is $1$ (Negative).
Invert bits: $000110$
Add $1$ : $000110 + 1 = 000111$
Decimal value: $-(4 + 2 + 1) = -7$

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Explanation

1. For $1001$ ( $4$ bits):

MSB is $1$ (Negative).

Invert bits: $0110$

Add $1$ : $0110 + 1 = 0111$

Decimal value: $-(4 + 2 + 1) = -7$

2. For $11001$ ( $5$ bits):

MSB is $1$ (Negative).

Invert bits: $00110$

Add $1$ : $00110 + 1 = 00111$

Decimal value: $-(4 + 2 + 1) = -7$

3. For $111001$ ( $6$ bits):

MSB is $1$ (Negative).

Invert bits: $000110$

Add $1$ : $000110 + 1 = 000111$

Decimal value: $-(4 + 2 + 1) = -7$

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