ES210, Digital Design Lab
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Lab 8: 2-Bit by 2-Bit Binary Multiplier
A. Objectives
1. Learn what a binary multiplier is and how a binary multiplier operates.
2. Design a binary multiplier using half-adder and implement a binary multiplier on the protoboard.
3. Build the Verilog design and test bench programs for a binary multiplier and simulate it for the input and output
waveforms.
B. Introduction
Multiplication of binary numbers is similar to multiplication of decimal numbers. The multiplicand is multiplied by each
bit of the multiplier starting from the least significant bit. Each of the resulting partial products is shifted one position to
the left. The summation of these shifted partial products makes the final product (see Mano, ed. 5, Section 4.7).
A bit
0
0
1
1
B bit
0
1
0
1
Product A x B
0
0
0
1
2-bit by 2-bit Multiplier
Multiplicand
Multiplier
Partial product 1->
Partial product 2->
Carries of previous bit->
Final product bits->
Example
Bit 2^1
Bit 2^0
1
1
1
1
1
1
1
0
0
C1 = 0
C0 = 1
A1 and A0 bits->
B1 and B2 bits->
1
C3 = 1
1
1
C2 = 0
Decimal
Equivalent
=3
=3
=3
=6
=9
Note that the max product value of two 2-bit binary numbers requires 4 bit positions.
C. Parts needed






A Digital Multimeter
A +5 V power supply
A breadboard/protoboard and wires
Two 7408 Quad 2-input AND gates
One 7486 Quad XOR gates
Datasheets of the gates from the Internet
D. Procedure
1. Fig. 1 (below, from Fig. 4.15 in Mano ed. 5) shows a 2-bit (A1A0) by 2-bit (B1B0) binary multiplier. Express the bit
positions of the final product (C3, C2, C1, C0) in terms of A1, A0, B1, B0 with only AND and XOR gates in the
table below. Also express these product bits in terms of NOT, AND, OR gates. The subscript “0” in each case
represents the lowest significant bit (LSB).
Product Bit Positions
C0 =
C1 =
C2 =
C3 =
Product Bit Positions in terms of A1, A0, B1, B0
2. How many gates do you need for such a 2-bit by 2-bit multiplier?
Number of AND gates needed
Dr. Ali Kujoory
6/30/2016
Number of XOR gates needed
1
2. Redraw Fig.1, a 2-bit by 2-bit multiplier, with only AND and XOR gates in the table below. Let the instructor check it
for you to make sure you can connect it properly in the next section.
Fig. 1. Two-bit by two-bit binary multiplier
3. Connect your diagram on the breadboard. Use AND and XOR gates, 4 switches to represent A1, A0, B1, and B0
inputs, and 4 LEDs to display the status of the output product bits in proper order. Power up the circuit and check your
results for the following input binary combinations. Show the circuit to the instructor when in full operation.
Switches
A1
A0
B1
B0
0
0
0
0
1
0
0
1
1
1
1
0
1
1
1
1
Write the product binary bits C3C2C1C0 in
terms of the binary bits A1, A0, B1, and B0.
C3
Product Binary Bits
C2
C1
C0
Decimal equivalent of
product bits C3C2C1C0
4. To simulate the above circuit write a Verilog design program, called two_bit_multiplier.v, in the table below and
compile it to ensure it is error-free. Use G0, G1, G2, G3, etc., to identify instances of the AND gates and XOR1 and
XOR2, etc. Use w0, w1, w2, w3, etc., to identify the wires indicated.
5. Then, write the corresponding Verilog test bench program in the table below and compile it to ensure it is error-free.
Include all the 4 combinations for A1, A0, B1, B0 with 50 ms delay between each combination entry in the program.
6. Simulate the program to display the waveforms of the inputs and output bits C3, C2, C1, C0 and copy the display in the
table below. Show your displays to the instructor.
// two_bit_multiplier.v program module
// two_bit_multiplier_tb.v program module
Waveforms of inputs and outputs
E. Feedback/Comments (your comments will help improving this lab)
Was the instruction clear enough? Any error?
How difficult was it for you?
Do you have any observations to make?
F. Report
1. In the answers you obtained and the display of waveforms in the tables above. Do not include the unnecessary
paragraphs such as the objectives, instructions, and procedures.
2. Each member should submit her/his Verilog section in the report to make sure that every one does the Verilog program.
Dr. Ali Kujoory
6/30/2016
2