THE GATEBOOK

Normalization Lectures

We know what a full-adder and full-subtractor is. Now consider a 1-bit full adder/subtractor. The two input bits a and b are to be operated on, under the control of a signal k (k=0 for addition, k=1 for subtraction). Another input is for either the carry or borrow from the lower bit. The outputs include the result r(sum or difference) and for carry or borrow to the next higher bit.

This 4-input 2-output circuit is implemented using logic gates. The two outputs are functions of the four inputs . The number of prime implicants of r, number of essential prime implicants of r, number of prime implicants of , and number of essential prime implicants of , respectively, are . Then is ____?

r has 4 PI and all these four PI are EPI.

Cout has 5 PI and 5 EPI.

So, total 18.