Homework
Download the Logisim 2.7.1. 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.
1. Construct a truth table for the following:
F = (x + y)(x' + z')(y' + z')
2. Using truth tables, show that:
xz = (x+y)(x+y')(x'+z)
3. Do Exercise - The truth table for a Boolean expression is shown below. Write the Boolean expression in sum-of-products form.
|
x
|
y
|
z
|
F
|
|
0
|
0
|
0
|
1
|
|
0
|
0
|
1
|
1
|
|
0
|
1
|
0
|
1
|
|
0
|
1
|
1
|
0
|
|
1
|
0
|
0
|
1
|
|
1
|
0
|
1
|
1
|
|
1
|
1
|
0
|
0
|
|
1
|
1
|
1
|
0
|
4. Draw the combinational circuit that directly implements the following:
Boolean expression: F(x, y, z) = y' + xy + y'z.
5. Consider Table 3.10 (Parity Generator) in the textbook. The parity bit is a function of Boolean variables x, y, and z. Represent this parity function in the following ways:
|
x
|
y
|
z
|
Parity Bit
|
|
0
|
0
|
0
|
1
|
|
0
|
0
|
1
|
0
|
|
0
|
1
|
0
|
0
|
|
0
|
1
|
1
|
1
|
|
1
|
0
|
0
|
0
|
|
1
|
0
|
1
|
1
|
|
1
|
1
|
0
|
1
|
|
1
|
1
|
1
|
0
|
|
Table 3.10 - Parity Generator
|
a. As a Boolean algebra expression
b. As a combinational logic diagram (logic circuit)
6. Exercise - Complete the truth table for the following sequential circuit:
|
A
|
B
|
X
|
Next State
|
|
A
|
B
|
|
0
|
0
|
0
|
|
|
|
0
|
0
|
1
|
|
|
|
0
|
1
|
0
|
|
|
|
0
|
1
|
1
|
|
|
|
1
|
0
|
0
|
|
|
|
1
|
0
|
1
|
|
|
|
1
|
1
|
0
|
|
|
|
1
|
1
|
1
|
|
|
7. Complete the tutorial provided with Logisim 2.7.1. The tutorial is under the "Help" menu in Logisim. Insert a picture of the circuit, as drawn in Logisim, into your homework submission. Use the "Export Image" function in the "File" menu to save an image file and then insert that in your submission. Uncheck the "Printer View" box when exporting the image from Logisim. Do not provide the picture as a separate file.
8. For this problem, you are to design a simple combinational logic circuit and then use Logisim to simulate and test the circuit. The circuit is a 2-bit priority encoder with inputs X2 and X1 and outputs Y1 and Y0. The circuit behaves as follows:
- If X2X1 = 00, then Y1Y0 = 00 (no active input)
- If X2X1 = 01, then Y1Y0 = 01 (low-priority input, X1, is active)
- If X2X1 = 1-, then Y1Y0 = 10 (high-priority input, X2, is active)
Note that the value of input X1 does not matter if the high-priority input, X2, is active. Also, output combination Y1Y0 = 11 should never occur.
a. Give the truth table that shows outputs Y1 and Y0 as functions of inputs X2 and X1.
b. Give the Boolean algebra expressions for output Y1 and output Y0.
c. Simulate your circuit using Logisim. Label all inputs and the output. Test for all four input combinations. Insert a picture of the circuit, as drawn in Logisim, into your homework submission.
Uncheck the "Printer View" box when exporting the image from Logisim. Your picture should show the circuit with input combination X2X1 = 11. Do not provide the picture as a separate file.
9. Scavenger Hunt: The JK flip-flop is sometimes called the "Jump-Kill" flip-flop. Although disputed, according to some sources it was named "JK" after one of the engineers on the team that designed a JK flip-flop circuit. The engineer's initials were "JK." This engineer later won a Nobel Prize.
a. Who was this engineer?
b. Why did he receive the Nobel Prize?
Attachment:- Assignment File.rar