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# Digital-Grand Test -Q5

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+1 vote

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 $\dpi{100} c_{in}$ is for either the carry or borrow from the lower bit. The outputs include the result r(sum or difference) and $\dpi{100} c_{out}$ for carry or borrow to the next higher bit.

This 4-input 2-output circuit is implemented using logic gates. The two outputs $\dpi{100} r( k,a,b,c_{in} ), c_{out}( k,a,b,c_{in} )$  are functions of the four inputs $\dpi{100} k,a,b,c_{in}$. The number of prime implicants of r, number of essential prime implicants of r, number of prime implicants of $\dpi{100} c_{out}$, and number of essential prime implicants of $\dpi{100} c_{out}$, respectively, are $\dpi{100} P,Q,R,S$. Then $\dpi{100} P+Q+R+S$ is ____?

reshown Jun 12, 2020