ITPEC FE Morning April 2020 Question 1

+127 plus +126 — in 2's complement addition, overflow happens only when two operands of the same sign give a sum outside −128 to +127.

An 8-bit signed integer holds −128 to +127. Read each pair and add:

• •(a) 0111 1111 + 1111 1110: 127 + (−2) = 125
• •(b) 0111 1111 + 0111 1110: 127 + 126 = 253, above +127; the result bits 1111 1101 read as −3
• •(c) 1000 0000 + 0111 0000: −128 + 112 = −16
• •(d) 1111 1111 + 1111 1111: −1 + (−1) = −2

Only (b) adds two positives and gets a negative sign bit.

Answer (b)

Why not others:

• •(a) — the operands have opposite signs, so the sum lies between them and cannot leave the range; it is 125
• •(c) — again opposite signs; the sum −16 is well inside the range
• •(d) — the addition carries out of bit 7, but a carry out is not a signed overflow; dropping it leaves 1111 1110, which is −2 and correct

Key rule: Signed overflow occurs only when both operands have the same sign bit and the result's sign bit differs; the carry out of the top bit does not signal it.

Basic Theory · AI-written, may contain errors