Consider the following 8-bit signed integers x, y using sign-magnitude format is x = 10110100, y = 01001100. Which of the following operations results overflow?

The correct option is x - y.

Let us analyze the given 8-bit signed integers $x$ and $y$ represented in the sign-magnitude format.
In an 8-bit sign-magnitude representation, the most significant bit (MSB, the leftmost bit) represents the sign (0 for positive, 1 for negative), and the remaining 7 bits represent the magnitude of the number.

First, we decode the value of $x=10110100$:
The sign bit (MSB) is 1, which means $x$ is negative.
The magnitude bits are $0110100$.
Converting this magnitude to decimal:
$0\times 2^6+1\times 2^5+1\times 2^4+0\times 2^3+1\times 2^2+0\times 2^1+0\times 2^0=32+16+4=52$.
Therefore, $x=-52$.

Next, we decode the value of $y=01001100$:
The sign bit (MSB) is 0, which means $y$ is positive.
The magnitude bits are $1001100$.
Converting this magnitude to decimal:
$1\times 2^6+0\times 2^5+0\times 2^4+1\times 2^3+1\times 2^2+0\times 2^1+0\times 2^0=64+8+4=76$.
Therefore, $y=+76$.

For an 8-bit sign-magnitude representation, the range of representable integers is from:
$-(2^7-1)$ to $+(2^7-1)$, which is $-127$ to $+127$.
An arithmetic overflow occurs if the mathematical result of an operation falls outside this representable range of $[-127,+127]$.

Let us evaluate the operation x - y:
$x-y=-52-76=-128$.
Since $-128$ is strictly less than the minimum representable value of $-127$, this operation causes a negative overflow.

For completeness, let us check the other operations:
• $x+y=-52+76=+24$ (Within range)
• $-x+y=-(-52)+76=52+76=+128$ (This would also overflow, but $x-y$ is the designated correct option)
• $-x-y=-(-52)-76=52-76=-24$ (Within range)

Thus, the operation x - y results in overflow.