Adder–subtractor
Computing circuit
In digital circuits, an adder–subtractor is a circuit that is capable of adding or subtracting numbers (in particular, binary). Below is a circuit that adds or subtracts depending on a control signal. It is also possible to construct a circuit that performs both addition and subtraction at the same time.
Construction
Having an n-bit adder for A and B, then S = A + B. Then, assume the numbers are in two's complement. Then to perform B − A, two's complement theory says to invert each bit of A with a NOT gate then add one. This yields S = B + A + 1, which is easy to do with a slightly modified adder.
By preceding each A input bit on the adder with a 2-to-1 multiplexer where:
Input 0 (I0) is A
Input 1 (I1) is A
that has control input D that is also connected to the initial carry, then the modified adder performs
addition when D = 0, or
subtraction when D = 1.
This works because when D = 1 the A input to the adder is really A and the carry in is 1. Adding B to A and 1 yields the desired subtraction of B − A.
A way you can mark number A as positive or negative without using a multiplexer on each bit is to use an XOR gate to precede each bit instead.
The first input to the XOR gate is the actual input bit
The second input for each XOR gate is the control input D
This produces the same truth table for the bit arriving at the adder as the multiplexer solution does since the XOR gate output will be what the input bit is when D = 0 and the inverted input bit when D = 1.
Begin with the source’s own compact description: “Adder–subtractor” is computing circuit. The dossier treats that line as a proposition to test through Adder, subtractor and Computing, not as a finished interpretation.
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