Spring 2000

Computer Science 3410 - Solutions

Boolean Algebra and Logic Gates


  1. Express the complement of the following functions in sum of minterm.
    a) F(A,B,C,D) = E(0,2,6,11,13,14)

    b) F(x,y,z) = P(0,3,6,7)

  2. Convert the following to the other canonical forms:
    a) F(x,y,z) = E(1,3,7)

    b) F(A,B,C,D) = P(0,1,2,3,4,6,12)

  3. The sum of all the minterms of a Boolean function of n variables is equal to 1. Prove this statement for n=3 and suggest a procedure for a general proof.
  4. Show that the Inhibition operation is neither commutative nor associative


  5. Show that a positive logic NAND gate is a negative logic NOR gate and vice versa.


  6. An integrated-circuit logic family has NAND gates with a fan-out of 5 and buffer gates with fan-out of 10. Show how the output signal of a single NAND gate can be applied to 50 other NAND-gate inputs without overloading the output gate. Use buffers to satisfy the fan-out requirements.
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