Binary subtraction using adders

Our binary adder can already handle negative numbers as indicated in the section on binary arithmetic But we have not discussed how we can get it to handle subtraction. To see how this can be done, notice that in order to compute the expression x - y, we can compute the expression x + -y instead. We know from the section on binary arithmetic how to negate a number by inverting all the bits and adding 1. Thus, we can compute the expression as x + inv(y) + 1. It suffices to invert all the inputs of the second operand before they reach the adder, but how do we add the 1. That seems to require another adder just for that. Luckily, we have an unused carry-in signal to position 0 that we can use. Giving a 1 on this input in effect adds one to the result. The complete circuit with addition and subtraction looks like this:Our binary adder can already handle negative numbers as indicated in the section on binary arithmetic But we have not discussed how we can get it to handle subtraction. To see how this can be done, notice that in order to compute the expression x - y, we can compute the expression x + -y instead. We know from the section on binary arithmetic how to negate a number by inverting all the bits and adding 1. Thus, we can compute the expression as x + inv(y) + 1. It suffices to invert all the inputs of the second operand before they reach the adder, but how do we add the 1. That seems to require another adder just for that. Luckily, we have an unused carry-in signal to position 0 that we can use. Giving a 1 on this input in effect adds one to the result. The complete circuit with addition and subtraction looks like this: