ITPEC FE Morning April 2020 Question 1

Two's Complement Overflow — detect when adding two 8-bit signed integers causes overflow.

Overflow occurs only when both operands have the same sign and the result has the opposite sign.

8-bit signed range: -128 to +127.

• •(a) 0111 1111 (+127) + 1111 1110 (−2) = +125 → different signs → no overflow
• •(b) 0111 1111 (+127) + 0111 1110 (+126) = 253 > 127 → both positive, result wraps negative → overflow
• •(c) 1000 0000 (−128) + 0111 0000 (+112) = −16 → different signs → no overflow
• •(d) 1111 1111 (−1) + 1111 1111 (−1) = −2 → fits in range → no overflow

Key rule: Addition overflow is impossible when operands have different signs. Check only same-sign pairs: does the sum exceed +127 or go below -128?

AI-generated — may contain errors