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Ithaca College, Ithaca, New York


Problem Set 3

Due: 7 February 2005

  1. Reduce the following equations using algebraic reduction. Show all intermediate equations. You do not have to implement your equations in hdl.

  2. Reduce the following equation using k-maps Show the k-map used. You do not have to implement your equation in hdl.

    3. F(a,b,c) = a'b'cd' + a'b'cd + a'bcd' + a'bc'd' + a'bcd + abc'd'

  3. Given the following truth table, derive the simplest expression for F using k-maps. Show your work, including the k-maps and the resulting equation. You do not have to implement this in hdl.

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

  4. You are to design a combinational circuit that when given a 3-bit binary number as an input will produce a binary number equal to the square of the number as an output. The truth table for such a circuit follows. Find the simplest expressions for the output quantities in SOP form. You must provide an equation for each output variable. You do not have to implement your results.

     x   y   z   A   B   C   D   E   F 
    0 0 0 0 0 0 0 0 0
    0 0 1 0 0 0 0 0 1
    0 1 0 0 0 0 1 0 0
    0 1 1 0 0 1 0 0 1
    1 0 0 0 1 0 0 0 0
    1 0 1 0 1 1 0 0 1
    1 1 0 1 0 0 1 0 0
    1 1 1 1 1 0 0 0 1

  5. Design an 8-to-1 mux using only NAND gates and inverters. Implement your design in hdl and test it with the hardware simulator. You must turn in the resulting circuit to the Arch Turn-In/PS 3 folder on Nova . You must also turn in the k-map used in your design, the resulting equation, and a diagram that implements the equation.

  6. Design a circuit to implement the following truth table using a 4-to-1 mux. Implement your design in hdl and test it with the hardware simulator. You must turn in the resulting circuit to the Arch Turn-In/PS 3 folder on Nova . You must also turn in the k-map used in your design, the resulting equation, and a diagram that implements the equation.

    7.  A   B   C   F 
    0 0 0 0
    0 0 1 1
    0 1 0 1
    0 1 1 0
    1 0 0 1
    1 0 1 0
    1 1 0 0
    1 1 1 1

Last updated on 03 Feb 2005 by John Barr