Answer :
Final answer:
The question about calculating 185 - 122 in sign-magnitude format cannot be directly answered because both initial values exceed the 8-bit representation range of -128 to +127. Therefore, technically, the operation cannot happen as stated due to the constraints of representing these numbers in the 8-bit system, thus avoiding the overflow or underflow concern, which is relevant only when the result of an operation exceeds the representable range.
Explanation:
The question involves calculating 185 - 122 with the numbers represented as signed 8-bit decimal integers in sign-magnitude format and determining if there's overflow, underflow, or neither. First, it's important to note that in an 8-bit signed number representation, the range of numbers is from -128 to +127. The biggest positive number that can be represented is +127, and the smallest negative number is -128.
Both 185 and 122 cannot be directly represented in this format because 185 exceeds the positive limit of +127. Thus, in a strict sense, the task is unfeasible with the constraints given. However, assuming an abstract scenario where these numbers could be accommodatively represented, subtracting 122 from 185 would result in 63, which is within the range and could be normally represented without overflow or underflow. But remember, in actual 8-bit sign-magnitude representation, both initial values are out of bounds.
Therefore, the correct answer to the question, considering the limitations of 8-bit signed representation, is that the operation as stated cannot be accurately carried out due to the initial values exceeding the representable range. Overflow or underflow terms apply when a calculation's result cannot be represented within the range; in this scenario, the problem exists before the operation due to the values themselves being out of range.
Subtraction of signed 8-bit decimals 185 and 122 yields 63. No overflow or underflow occurs in this operation.
In signed 8-bit decimal integers, the range typically spans from -128 to 127.
Let's first convert 185 and 122 to their binary representations:
185:
- Decimal: 185
- Binary: 10111001
122:
- Decimal: 122
- Binary: 01111010
Now, let's perform the subtraction: 185 - 122
```
10111001 (185)
- 01111010 (122)
-----------
01011111 (63)
```
The result in binary is 01011111, which is equal to 63 in decimal.
Since both 185 and 122 are within the range of signed 8-bit integers (-128 to 127), there is no overflow or underflow in this subtraction.
