Homework: Digital Logic

 

  1. Construct the truth table for the following circuit.

  2. Construct the truth table for the following circuit.

  3. Write an algebraic expression for the following truth table and construct the logic circuit for the result.

     
    A    		  
    B    		  
    F
    0 0 1
    0 1 0
    1 0 1
    1 1 0

  4. Write an algebraic expression for the following truth table, simplify it, and construct the logic circuit for the result.

     
    A    		  
    B    		  
    C    		  
    F
    0 0 0 1
    0 0 1 0
    0 1 0 0
    0 1 1 1
    1 0 0 0
    1 0 1 0
    1 1 0 0
    1 1 1 1

  5. Given the following truth table, write the expressions for F1 and F2, simplify each expression, and draw one circuit to implement both functions.
  6. Construct the logic circuit for the function R(S + ST) + RT

  7. The class handout shows the circuit for a 2x4 decoder. Show the truth table for this decoder.

  8. Show the truth table for a 3x8 decoder.

  9. How many control lines does a multiplexer have if it has 32 data inputs?

  10. Here is a half adder represented with NAND gates. Complete the following truth table to prove that this circuit correctly represents a half adder.
    A B (1) (2) (3) Sum Carry
                 

  11. Given the following circuit:

    1. What is the equivalent Boolean expression?

    2. Show the truth table

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