Assume 185 and 122 are signed 8-bit decimal integers stored in sign-magnitude format. Calculate the result of 185 + 122. Is there overflow, underflow, or neither?

Question

19-03-2024
Mathematics

High School

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Assume 185 and 122 are signed 8-bit decimal integers stored in sign-magnitude format. Calculate the result of 185 + 122. Is there overflow, underflow, or neither?

Answer :

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ayanqureshi21 ayanqureshi21 · Answer 1 · 2025-01-25T00:58:46-05:00

Final answer:

The calculation of 185 - 122 using signed 8-bit decimal integers in sign-magnitude format results in overflow because 185 is outside of the range representable by signed 8-bit integers (-127 to +127).

Explanation:

The question revolves around the calculation of the expression 185 - 122 using signed 8-bit decimal integers in sign-magnitude format, and determining if there is overflow or underflow. Signed 8-bit integers can represent values from -127 to +127. In sign-magnitude format, the most significant bit (MSB) represents the sign (0 for positive, 1 for negative), and the remaining bits represent the magnitude of the number.

To represent 185 in an 8-bit signed integer, it would exceed the maximum positive value of +127, leading to overflow. Therefore, it's not possible to represent the number 185 with only 8 bits in sign-magnitude format. For 122, however, the number is within range, and its 8-bit sign-magnitude representation would be 01111010, with the first 0 indicating a positive number.

Because 185 cannot be represented with an 8-bit signed integer in sign-magnitude format, the calculation cannot be performed, and an overflow error occurs even before any operation takes place.