If you would like to play around with this circuit yourself, the link to the circuit in Logisim can be found here.īuilding the full ALU can be a very tedious process, but it is incredibly important to keep things organized! The images on the right detail the different operations of addition vs subtraction. This implementation can be seen in the diagram on the left. When the line goes HIGH (indicating subtraction), it will add one through the carry-in. As for adding one, we can run this same subtraction/addition line into the very first carry-in input to the first full adder circuit. If we have 8 XOR gates and the first input into all of them is the corresponding B digit and the second input was a wire that we controlled to activate subtraction/addition, running the wire HIGH would invert the output of all gates (check the logic table for XOR gates earlier). We need a way of inverting all B inputs on command to signal subtraction. With all digits inverted, we get: 11100011Īs such, -B = 11100100 which is (-28 in decimal - two's complement).The method involves first inverting all the numbers in B.Using two's-complement, a number system that allows us to represent negative numbers in binary, we can change B to -B. Subtracting numbers, say A - B, is the same as adding A + (-B).

Luckily, there is a relatively straight-forwarded solution to this. However, so far we have only discussed addition. Our ALU should be able to add and subtract 8-bit numbers. As such, the design above demonstrates the configuration of 8 full adder circuits where the carry is passed on from each full adder and into the next. As mentioned in the step above, our 8-bit ALU requires an 8-bit adder for each of the 8 binary values.

8 bit full adder truth table