Introduction:
In a ripple carry adder, the sum output takes some time to stabilize after the inputs change. This time delay is known as latency. The latency of an 8-bit ripple carry adder depends on the inputs A and B. In this case, we are given that A is represented by the decimal value 1. We need to determine the value of B that leads to the longest latency for the sum to stabilize.

Understanding 2's Complement:
Before we proceed, let's understand how integers are represented in 2's complement form. In 2's complement, the most significant bit (MSB) represents the sign of the number. If the MSB is 0, the number is positive, and if the MSB is 1, the number is negative. To obtain the 2's complement of a negative number, we invert all the bits and add 1 to the resulting value.

Calculating the Sum:
To calculate the sum of A and B, we need to add these two numbers in their 2's complement form. Since A is represented by the decimal value 1, its 2's complement form is 00000001.

Now, let's consider B as -1. To represent -1 in 8-bit 2's complement, we start by converting 1 to binary: 00000001. Then, we invert all the bits to get the 2's complement: 11111110. Therefore, B is represented as 11111110.

Determining the Longest Latency:
To determine the longest latency, we need to consider the worst-case scenario for the ripple carry adder. This occurs when the carry bit has to propagate through all the stages of the adder.

In this case, since B is -1 (represented as 11111110), the MSB of B is 1. When adding A and B, the MSB of the sum will depend on the carry generated by the addition of the MSB bits.

In the worst-case scenario, the carry generated by the addition of the MSB bits will propagate through all the stages, causing a delay in the stabilization of the sum output. This delay is the longest latency we are looking for.

Conclusion:
Therefore, the value of B that leads to the longest latency of the sum to stabilize is B = -1.