NIMCET 2007 — Computer PYQ

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Question

NIMCET 2007 — Computer PYQ

NIMCET | Computer | 2007

Zero has two representations in:

Choose the correct answer:

Explanation

In digital logic and computer science, representing signed integers in binary code can be achieved through multiple methods. Let us analyze how the number $0$ is represented under an $n$ -bit system across the options.

1. Sign-Magnitude Representation

In a sign-magnitude system, the Most Significant Bit (MSB) acts strictly as a sign indicator ( $0$ for positive, $1$ for negative), while the remaining $n - 1$ bits encode the actual magnitude.

Positive Zero ( $+ 0$ ): The MSB is $0$ . For an $8$ -bit sequence, this looks like $0000000 0_{2}$ .
Negative Zero ( $- 0$ ): The MSB is $1$ . For an $8$ -bit sequence, this looks like $1000000 0_{2}$ .

Because $+ 0 \neq = - 0$ in their bit patterns, sign-magnitude has two representations for zero.

2. 1's Complement Representation

In 1's complement, negative values are computed by flipping every bit of their positive counterpart.

Positive Zero ( $+ 0$ ): Represented as all zeros, i.e., $0000000 0_{2}$ .
Negative Zero ( $- 0$ ): Created by bitwise inverting $+ 0$ , resulting in all ones, i.e., $1111111 1_{2}$ .

Because these two distinct bit patterns both map mathematically to zero, 1's complement has two representations for zero.

3. 2's Complement Representation

In 2's complement, negative numbers are generated by taking the 1's complement and adding $1$ .

Positive Zero ( $+ 0$ ): Represented as $0000000 0_{2}$ .
Negative Zero ( $- 0$ ):
$1’s complement of 0 = 1111111 1_{2}$
$Add 1 = 1111111 1_{2} + 1_{2} = 10000000 0_{2}$
Since it is an $8$ -bit register, the extra carry bit on the far left overflows and is discarded, leaving $0000000 0_{2}$ .

Thus, $+ 0$ and $- 0$ share the exact same binary pattern. 2's complement has only one unique representation for zero.

Ambiguity Note on the Options

Both (a) sign magnitude and (b) 1's complement explicitly feature dual representations for zero. In multiple-choice questions where only a single option must be picked, sign magnitude is typically designated as the primary historical example of this architectural drawback, though both options technically satisfy the condition.

Correct Answer: (a) sign magnitude (and (b) 1's complement)