Full Subtractor

The circuit performs the mathematical operation of subtraction on three binary digits. The three digits are Minuend (MD), Subtrahend (SD), and Borrow Input (BI). The subtrahend and the borrow input are subtracted from minuend generating Difference (DIFf) and Borrow Output (BOf) as output signals. The DIFf output bit will be set if the number of input bits set to 1 is odd. Thus the DIFf output can be generated by a three-input Exclusive OR (XOR) gate. The borrow output (BOf) bit will be set on one of these conditions: ∙ The subtrahend or/and the borrow input is/are 1 when minuend is 0. That is, minuend is 0 and at least one of the other two input signals is 1. ∙ The subtrahend and the borrow input are both 1. Note that for the second condition the state of minuend is irrelevant so the first and second conditions overlap when minuend is 0 and the other two input signals are both 1. Then, a three-input majority voting logic can be used for borrow output if minuend is inverted first. Variables / Signal Names: BI = Borrow Input MD = Minuend SD = Subtrahend DIFf = (Full subtractor) Difference BOf = (Full subtractor) Borrow Output