JAMIA 2025 — Computer PYQ

1. Analysis of the Systems

A. Sign-Magnitude Representation

In this system, the most significant bit (MSB) is the sign bit ($0$ for positive, $1$ for negative), and the remaining bits represent the magnitude.

• Positive Zero: Sign bit is $0$.

• Negative Zero: Sign bit is $1$.

  For an 8-bit number:

  $$\text{Positive Zero}=00000000$$
  $$\text{Negative Zero}=10000000$$

B. 1’s Complement Representation

In 1's complement, negative numbers are created by inverting all bits of the positive number.

• Positive Zero: All bits are $0$.

• Negative Zero: All bits are $1$ (inverted positive zero).

  For an 8-bit number:

  $$\text{Positive Zero}=00000000$$
  $$\text{Negative Zero}=11111111$$

2. Why 2’s Complement is Different

In 2’s Complement (the system used by most modern computers), there is only one unique representation for zero. When you try to find the negative of zero using the 2's complement rule (Invert + 1):

1. Take $+0$: $00000000$

2. Invert bits: $11111111$

3. Add $1$: $11111111+1=100000000$

4. Discard the carry bit: $00000000$

The result is identical to the original, so:

Conclusion

Both (A) Sign Magnitude and (B) 1’s Complement have two representations for zero. If this is a multiple-choice question where only one can be picked, it is often a trick or there is an "Both A and B" option missing. However, technically:

Both (A) and (B) are correct.