n an addition operation, an overflow is possible when both numbers are positive or when both numbers are negative.Group of answer choicesTrueFalse

Evaluating the Statement

1. Break Down the Problem

   • The statement claims that an overflow can occur during addition when both operands are positive or both are negative.

2. Relevant Concepts

   • Overflow in Addition: In binary arithmetic, overflow occurs when the result of an addition exceeds the maximum representable value for a given number of bits.
   • For positive numbers, if the sum exceeds the maximum representable positive number (which normally occurs in systems using signed integers):
     • e.g., For an 8-bit signed integer, the range is from -128 to 127. Adding two large positive numbers could exceed 127.
   • For negative numbers, similar logic applies: if the sum of two large negative values exceeds the minimum representable negative number, overflow can occur.

3. Analysis and Detail

   • When both numbers are positive (e.g., adding 100 + 50):
     • The result is 150, which may exceed the maximum for the chosen integer type.
   • When both numbers are negative (e.g., adding -100 + -50):
     • The result is -150, which may exceed the minimum for the chosen integer type, causing overflow.

4. Verify and Summarize

   • Both scenarios (positive + positive and negative + negative) lead to potential overflow situations. Therefore, the statement is indeed true.

Final Answer

True: An overflow is possible in an addition operation when both numbers are positive or when both numbers are negative.