Spring 2000

Computer Science 3410 - Solutions

Simplification of Boolean Functions


It will be beneficial to use MAX+plus II to draw the logic diagrams in the following questions.

  1. Draw a logic diagram using only two-input NAND gates to implement the following expression:   (AB + A'B')(CD' + C'D)


  2. Implement the following functions with three-level NOR gate circuits:
    a) F = wx' + y'z' + w'yz'    
    b) F(w,x,y,z) = E(5,6,9,10)   

  3. Implement the following functions with three-level NAND gate circuits:
    a) AB' + ABD + ABD' + A'C'D' + A'BC'    
    b) BD + BCD' + AB'C'D'    

  4. Find eight different two-level gate circuits to implement F = xy'z + x'yz + w


  5. Implement the function F(A,B,C,D) = E (0,1,2,3,4,8,9,12) with the following two-level forms: NAND-AND and NOR-OR
       

  6. Implement the following Boolean function F together with the don't-care conditions d using no more than NOR gates. Assume that both the normal and complement inputs are available.

    F(A,B,C,D) = E (0,1,2,9,11)
    d(A,B,C,D) = E (8,10,14,15)



  7. Using Alternate forms of K-maps : Simplify the Boolean function
    F = E (1,2,3,5,7,9,10,11,13,15) using the two maps below.


            
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