Logisim 2.7.1: Download, Tutorial, Truth Tables, and Circuit Design

• Download the Logisim 2.7.1 from http://sourceforge.net/projects/circuit/. Logisim is a simple
logic simulator designed for educational use. Pick the platform appropriate for your
computer. You will need Logisim for this homework and later assignments. More information
about Logisim is available at http://www.cburch.com/logisim/.

Homework 2 consists of the following problems.
1. Construct a truth table for the following:
F = (x + y)(x' + z')(y' + z')
X Y Z (x+y) (x’+ z’) (y’+ z’) F
0 0 0 0 1 1 0
0 0 1 0 1 1 0
0 1 0 1 1 1 1
0 1 1 1 1 0 0
1 0 0 1 1 1 1
1 0 1 1 0 1 0
1 1 0 1 1 1 1
1 1 1 1 0 0 0
2. Using truth tables, show that:
xz = (x+y)(x+y’)(x’+z)
X Y Z (x+y) (x+ y’) (x’+ z) F xz
0 0 0 0 1 1 0 0
0 0 1 0 1 1 0 0
0 1 0 1 0 1 0 0
0 1 1 1 0 1 0 0
1 0 0 1 1 0 0 0
1 0 1 1 1 1 1 1
1 1 0 1 1 0 0 0
1 1 1 1 1 1 1 1

Truth table for #3
3. The truth table for a Boolean expression
is shown. Write the Boolean expression
in sum-of-products form.
F = (x’y’z’) + (x’y’z) + (xy’z) + (xyz) 0
0
1
4. Draw the combinational circuit that
directly implements the following Boolean expression:
F(x,y,z) = y’ + xy + y’z.