Question

Perform the following 8 bit binary arithmetic operations. For

each problem, indicate whether overflow/underflow occurs.
1 00101101
+ 01101100
2 00001110
- 00110101
3 00011111
+ 01010101
4 10110011
- 0

Answer 1

1. \(00101101_2 + 01101100_2 = 100110101_2\); No overflow/underflow occurs.

2. \(00001110_2 - 00110101_2 = 11011001_2\); Overflow occurs.

3. \(00011111_2 + 01010101_2 = 01110100_2\); No overflow/underflow occurs.

4. \(10110011_2 - 0_2 = 10110011_2\); No overflow/underflow occurs.

Step-by-step explanation:

1. In the first operation, addition of \(00101101_2\) and \(01101100_2\) yields \(100110101_2\) without any overflow or underflow because the sum doesn't exceed the capacity of 8 bits.

2. For the second operation, subtracting \(00110101_2\) from \(00001110_2\) results in \(11011001_2\). This is an overflow since the subtraction produces a negative result in 8-bit signed binary, indicating that the result is beyond the representable range.

3. In the third operation, adding \(00011111_2\) and \(01010101_2\) results in \(01110100_2\) without any overflow or underflow.

4. Lastly, subtracting \(0_2\) from \(10110011_2\) gives \(10110011_2\) without overflow or underflow since subtracting zero doesn't alter the value.

Understanding overflow/underflow is crucial in binary arithmetic, especially in fixed-width systems where the result might go beyond the capacity of the given number of bits. Overflow occurs when the result exceeds the maximum representable value, while underflow occurs when the result is less than the minimum representable value.