IMPLEMENTATION OF A BOOLEAN EXPRESSION 1
0.1 Experiment 2 (Implementation of a Boolean Expression)
0.1.1 Aim
In this experiment, your knowledge to minimize the number of gates by using decoder and multiplexer gate.
0.1.2 Problem
A circuit takes five inputs denoted as x4,x3,x2,x1, and x0. This circuit has only one output y. The output is determined as shown in the following table.
x4
x3
y
0
0
PRIME?(x2,x1,x0)
0
1
EVEN?(x2,x1,x0)
1
0
MAJ?(x2,x1,x0)
1
1
EQ?(x2,x1,x0)
We define PRIME, EVEN, MAJ, and EQ as follows. x2x1x0 represents a three bit unsigned number.
PRIME?(x ,x ,x ) = 1 x2x1x0 is prime
otherwise
EV EN?(x ,x ,x ) = 1 x2x1x0 is even
otherwise
Most of x2,x1,x0 are 1 otherwise
1 x2 = x1 = x0 otherwise
You are only allowed to use one 2x4 Decoder, one 8x1 Multiplexer, at most 2
binary logic gates (AND, OR, XOR, XNOR, NAND, NOR) and infinite number of NOT gates to complete the design of this circuit.
0.1.3 Preliminary Work
Before the experiment, you should prepare following materials:
1. Fill the truth table.
2. Draw the circuit of your design.
3. Write a verilog code for the circuit drawn in the previous step. Verilog codeshould have two components. First, you have to write behavioural level verilog code which implements the functionality of multiplexer and/or decoder. Then, you have to write the gate level verilog code (source.v) for your circuitry which uses the implemented components and additional built-in gates (i.e. AND, OR, NAND, NOR, XOR, or XNOR).
2
4. Write the verilog code for the testbench (testbench.v) in order to test all possibleinput combinations.
Then, submit the your code, and your report under the name <StudentID1 <StudentID2 PRE2.zip through Moodle.
