logical-operatorscircuit

What is B supposed to turn into in this 8-bit adder?


An image of a logical circuit with two 8-bit adders where as one of them takes A and B

I understand that it takes 4A and subtracts it from B but the two appended 1s that are added to B make it difficult for me to understand. What am I subtracting from 2A? 1B1?

I couldn't find any examples with similar inputs either. The answer key says it's supposed to be 2B but I do not think they are similar in any way, unless there is something I am missing?


Solution

  • Maybe this example with specific values will clarify the situation?

    A is multiplied by 4: 4A.
    B is inverted 63 - B, multiplied by 2 and added 128 + 1 = 129: 2(63 - B) + 129 = 255 - 2B. If we consider these 1s as part of an inversion, that will lead to the same result: 255 – 2B.
    The first adder result taking into account Cin: 255 – 2B + 4A + 1 = 256 - 2B + 4A. Since it is 8-bit, that leaves 4A - 2B.
    The second adder subtracts 1 from the result if it is negative.

    enter image description here