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 -179. The calculation results in overflow.

Step-by-step solution

Perform the calculation 185 - 122

With 8-bit sign magnitude, the most significant bit of the integer is used for sign representation. The most significant bit equal to 0 represents the positive number. The most significant bit equals to 1 represents the negative number. The binary representation of 185 is 10111001, which is a negative number, with decimal equivalent -57. The binary representation of 122 is 01111010, which is a positive number, with decimal equivalent 122. The calculation of -57 – 122 results in -179. Hence, the result of 185-122 is -179.

Check if the calculation results is overflow or underflow

If the result of the operation requires more bits than available to represent the data in the memory, then overflow occurs. The resulted value is -179. The value of -179 cannot be represented using sign magnitude of 8-bit decimal integer. With 8-bit decimal integer, the most-significant bit is used to represent sign and 179 cannot be represented using 7-bits. Hence, the overflow occurs.