1. Lab 3 : Multiplier
Overview

2. Lab 3 : Multiplier Create a 2 x 2 bits multiplier using:
K-Map Technique
Array Technique
Create a 4x4 bit multiplier using the 2x2 bit multiplier

3. Part A : K-Map Technique
Create a Truth Table for 2 bit “multiplier” and 2 bit “multiplicand”
Input (Multiplier) = A1 and A0
Input (Multiplicand) = B1 and B0
Output = 4 bit = S3, S2, S1 and S0 (example)
Using K-Map, obtain the boolean expression for each output.
Draw the schematic diagram
Transfer in Altera Max+Plus II using the Graphic Editor
Submit : Truth Table, K-Map, Boolean Expression, Printed Schematic and Printed Waveform

4. Part A : K-Map Technique
Simulate your design
Input A1 and A0 = fix value (repeat for 4 levels)
Input B1 and B2 = counting sequence
Study the waveform

5. Part A : K-Map Technique
Check and study the timing Analyzer for time delay
Go to : Max+PlusII > Timing Analyzer

6. Part B : Array Technique
Create the 2x2 multiplier using Full ADDERS.
Still remember the truth table for ADDERS?!!??

7. Full Adder Full Adder Truth Table S = X Å Y Å (C-in) X 1 Y S C-out
Inputs
Outputs X 1 Y S
C-out
C-in
C-out = XY + X(C-in) + Y(C-in)
Full
Adder X Y S
C-in
C-out
S(X,Y, C-in) = S (1,2,4,7)
C-out(x, y, C-in) = S (3,5,6,7)

8. Full Adder
Full adder can also be implemented using 2 x ½ ADDER and one OR gate. (check in ref. book how it is done??)

9. Half Adder X 1 Y S C-out Half Adder Truth Table: S = X Å Y C-out = XY1 Y S
C-out
Half Adder Truth Table:
Inputs
Outputs
S = X Å Y
C-out = XY X Y
Sum S
Half
Adder X Y S
C-OUT
C-out

10. Part B : Array Technique
Submit your drawings of full adders and its truth table, your printed schematic, and waveform (same input and as K-Map technique)
Fill in the timing analyzer

11. K-Map Vs Array After Analyzing your timing and getting the time delay
NOW. Check your delay:
K-Map = what is the delay?
Array Technique = what is the delay?
Why??? (Conclusion)

12. 2 x 2 Multiplier using Array technique – The Concept
A1 A0
B1 B0 x C C
A1B0 A0B0 +
A1B1 A0B1 S3 S2 S1 S0

13. THE CHALLENGE Part C : 4 x 4 Multiplier
Design 4 x 4 bits multiplier using Array technique
Use the Multiplier 2x2 symbols and full adders which u have created.
Hints : Look back at the concept of 2x2 multiplier. Take the same step.

14. Part C : 4 x 4 Multiplier Simulate your waveform
Submit your printed schematic diagram and waveform

15. Max+PlusII Tips
Bus line
A[3..0] A3 A2 A1 A0

16. Part C : 4 x 4 Multiplier Extra Activity
Download your 4x4 multiplier to UP2 board using FPGA (Flex10K)
Pin Configuration to input
(use flex switch 1-8)
Pin Configuration to output
(use flex digit 1 & 2 )
4x4
Multiplier
(your design)
Tenth & Unit
Segment
Decoder
7447
BCD to
7Seg
a - g A0 A1 A2 A3 B0 B1 B2 B3

17. Do first thing first Important? Urgent?
THANK YOU
Do first thing first
Important?
Urgent?