Question

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

Short answer

The value of 185+122 is 65. In this calculation, there is neither overflow nor underflow.

Step-by-step solution

Convert 185 and 122 8-bit decimal integers to binary

The 8-bit decimal integers are stored in sign-magnitude format. In sign-magnitude format, the most significant bit is reserved for the sign. If the most-significant bit is 1, the number is negative. Otherwise, the number of positive. The binary form of 185 is 10111001. The most significant bit is 1. So, the number is negative and is equal to -57. The binary form of 122 is 01111010. The most significant bit is 0. So, the number is positive.

Perform the calculation 185+122

The actual decimal value of 185 8-bit integer stored in sign-magnitude is -57. The value of 122 is same in the decimal format because it is a positive number. The calculation of -57+122 results in 65. The binary of 65 is 01000001. Hence, the calculation of 185+122 results in 65.

Identify if there is overflow or underflow

Overflow occurs if the result of the operation needs more bits to store it in the memory than available in the hardware. Underflow occurs if the result of the operation requires smaller number of bits than available to store it in the memory. The result of the operation 185+122 is 65 which is stored in 8-bit integers with sign magnitude as 01000001. Hence, there is neither overflow nor underflow.