Consider the 8-bit signed integers 𝑋,π‘Œ and 𝑍 represented using the…

2026

Consider the 8-bit signed integers 𝑋,π‘Œ and 𝑍 represented using the sign-magnitude form. The binary representations of 𝑋 and π‘Œ are as follows:

X: 10110100 π‘Œ: 01001100

Which of the following operations to compute 𝑍 result(s) in an arithmetic overflow?

  1. A.

    Z=𝑋+π‘Œ

  2. B.

    Z=𝑋-π‘Œ

  3. C.

    Z=-𝑋+π‘Œ

  4. D.

    Z=-𝑋-π‘Œ

Attempted by 18 students.

Show answer & explanation

Correct answer: B, C

Solution

Step 1: Convert binary to decimal. X = 10110100 (Sign-Magnitude) = -52. Y = 01001100 = +76.

Step 2: Determine range. 8-bit signed magnitude range is -127 to +127.

Step 3: Evaluate operations. A: -52 + 76 = 24 (Valid). B: -52 - 76 = -128 (Overflow). C: 52 + 76 = 128 (Overflow). D: 52 - 76 = -24 (Valid).

Step 4: Conclusion. Operations B and C result in overflow.

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