Lab 3 : MultiplierLab 3 : Multiplier

OverviewOverview

Lab 3 : MultiplierLab 3 : Multiplier

Create a 2 x 2 bits multiplier using:Create a 2 x 2 bits multiplier using: K-Map TechniqueK-Map Technique Array TechniqueArray Technique

Create a 4x4 bit multiplier using the Create a 4x4 bit multiplier using the 2x2 bit multiplier2x2 bit multiplier

Part A : K-Map Part A : K-Map TechniqueTechnique

Create a Truth Table for 2 bit “multiplier” and 2 Create a Truth Table for 2 bit “multiplier” and 2 bit “multiplicand”bit “multiplicand” Input (Multiplier) = A1 and A0Input (Multiplier) = A1 and A0 Input (Multiplicand) = B1 and B0Input (Multiplicand) = B1 and B0 Output = 4 bit = S3, S2, S1 and S0 (example)Output = 4 bit = S3, S2, S1 and S0 (example)

Using K-Map, obtain the boolean expression for Using K-Map, obtain the boolean expression for each output.each output.

Draw the schematic diagramDraw the schematic diagram Transfer in Altera Max+Plus II using the Graphic Transfer in Altera Max+Plus II using the Graphic

EditorEditor Submit : Truth Table, K-Map, Boolean Expression, Submit : Truth Table, K-Map, Boolean Expression,

Printed Schematic and Printed WaveformPrinted Schematic and Printed Waveform

Part A : K-Map Part A : K-Map TechniqueTechnique

Simulate your designSimulate your design Input A1 and A0 = fix value (repeat for 4 levels)Input A1 and A0 = fix value (repeat for 4 levels) Input B1 and B2 = counting sequenceInput B1 and B2 = counting sequence

Study the waveformStudy the waveform

Part A : K-Map Part A : K-Map TechniqueTechnique

Check and study the timing Analyzer for time Check and study the timing Analyzer for time delaydelay

Go to : Max+PlusII > Timing AnalyzerGo to : Max+PlusII > Timing Analyzer

Part B : Array TechniquePart B : Array Technique

Create the 2x2 multiplier using Full Create the 2x2 multiplier using Full ADDERS.ADDERS.

Still remember the truth table for Still remember the truth table for ADDERS?!!??ADDERS?!!??

Full AdderFull Adder

X00001111

Y00110011

S01101001

C-out 0 0 0 1 0 1 1 1

C-in 0 1 0 1 0 1 0 1

Full Adder Truth Table

S(X,Y, C-in) = (1,2,4,7)C-out(x, y, C-in) = (3,5,6,7)

Inputs Outputs S = X Y (C-in)

C-out = XY + X(C-in) + Y(C-in)

Full Adder

X Y

S

C-inC-out

Full AdderFull Adder

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

Half AdderHalf Adder

X0011

Y0101

S0110

C-out 0 0 0 1

Half Adder Truth Table:

Inputs Outputs

S = X Y

C-out = XY

X

YSum S

C-out HalfAdder

X

Y

SC-OUT

Part B : Array TechniquePart B : Array Technique

Submit your drawings of full adders Submit your drawings of full adders and its truth table, your printed and its truth table, your printed schematic, and waveform (same schematic, and waveform (same input and as K-Map technique)input and as K-Map technique)

Fill in the timing analyzerFill in the timing analyzer

K-Map Vs ArrayK-Map Vs Array

After Analyzing your timing and After Analyzing your timing and getting the time delaygetting the time delay

NOWNOW. Check your delay:. Check your delay: K-Map = what is the delay?K-Map = what is the delay? Array Technique = what is the delay?Array Technique = what is the delay?

Why??? (Conclusion)Why??? (Conclusion)

2 x 2 Multiplier using Array 2 x 2 Multiplier using Array technique – The Concepttechnique – The Concept

A1 A0B1 B0x

A1B0 A0B0A1B1 A0B1+

S0S1S2S3

CC

Part C : 4 x 4 MultiplierPart C : 4 x 4 Multiplier

THE CHALLENGETHE CHALLENGE Design 4 x 4 bits multiplier using Design 4 x 4 bits multiplier using

Array techniqueArray technique Use the Multiplier 2x2 symbols and Use the Multiplier 2x2 symbols and

full adders which u have created.full adders which u have created. Hints : Look back at the concept of Hints : Look back at the concept of

2x2 multiplier. Take the same step.2x2 multiplier. Take the same step.

Part C : 4 x 4 MultiplierPart C : 4 x 4 Multiplier Simulate your waveformSimulate your waveform Submit your printed schematic diagram and Submit your printed schematic diagram and

waveformwaveform

Max+PlusII TipsMax+PlusII Tips

Bus lineBus line

A3A2A1A0

A[3..0]

Part C : 4 x 4 MultiplierPart C : 4 x 4 MultiplierExtra ActivityExtra Activity

Download your 4x4 multiplier to UP2 Download your 4x4 multiplier to UP2 board using FPGA (Flex10K)board using FPGA (Flex10K)

4x4 Multiplier

(your design)

Tenth & UnitSegmentDecoder

7447BCD to

7Seg

7447BCD to

7Seg a - g

a - g

A0A1A2A3

B0B1B2B3

Pin Configuration to input(use flex switch 1-8)

Pin Configuration to output(use flex digit 1 & 2 )

THANK YOUTHANK YOU

Do first thing firstDo first thing firstImportant?Important?

Urgent?Urgent?