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ECEn/CS 224

MultiplexersDecoders

ROMs (LUTs)

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ECEn/CS 224

A Problem Statement

Design a circuit which will select

between two inputs (A and B) and pass

the selected one to the output (Q).

The desired circuit is called a multiplexer or MUX for short

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ECEn/CS 224

Multiplexers

q = s’a + sb

0

1

0

1

a

b

s

q

a

b

s

q

s a b q

0 0 0 00 0 1 00 1 0 10 1 1 11 0 0 01 0 1 11 1 0 01 1 1 1

Preferred symbol

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ECEn/CS 224

0

1

a

b

1

q0

1

a

b

0

q

Data Steering

0

1

a

b

s

q

Key idea: select wire selects one of the inputs and passes it out to the output.

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ECEn/CS 224

A 4:1 MUX

4:1MUX

I0

I1

I2

I3

Z

A B

DataInputs

Control Inputs

Output

Z = A’B’I0 + A’BI1 + AB’I2 + ABI3

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ECEn/CS 224

A General MUX

n:1MUX

I0

I1

…

In-1

Z

sk-1 …. s0

n DataInputs

log2(n) Control Inputs

Output

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ECEn/CS 224

Implementing Logic with MUX Blocks

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ECEn/CS 224

Example 1

A B C F0 0 0 00 0 1 00 1 0 00 1 1 01 0 0 01 0 1 11 1 0 11 1 1 1

A=0 part of the truth table … when A=0, F=0

A=1 part of the truth table … when A=1, F=B+C

0

1

0

B+C

A

F

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ECEn/CS 224

Example 2

B A C F0 0 0 00 0 1 00 1 0 00 1 1 11 0 0 01 0 1 01 1 0 11 1 1 1

B=0 part of the truth table … when B=0, F=AC

B=1 part of the truth table … when B=1, F=A

0

1

AC

A

B

F

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ECEn/CS 224

Example 3C A B F0 0 0 00 0 1 00 1 0 00 1 1 11 0 0 01 0 1 01 1 0 11 1 1 1

C=0 part of the truth table … when C=0, F=AB

C=1 part of the truth table … when C=1, F=A

0

1

AB

A

C

F

All 3 of these examples are the same truth table…

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ECEn/CS 224

Using a Bigger MUX

A B C F0 0 0 00 0 1 00 1 0 10 1 1 01 0 0 11 0 1 11 1 0 01 1 1 1

AB=00 part of the truth table … when AB=00, F=0

AB

FAB=01 part of the truth table … when AB=01, F=C’AB=10 part of the truth table … when AB=10, F=1AB=11 part of the truth table … when AB=11, F=C

00

01

10

11

0C’1C

Can easily re-order truth table to use different MUX control inputs

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ECEn/CS 224

Another 4:1 MUX Example

A B F0 0 10 1 11 0 01 1 1

AB

F00

01

10

11

1101

This shows that a large enough MUX can directly implement a truth table…

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ECEn/CS 224

MUX for Logic - Alternate Method

AB

F00

01

10

11

0C’1C

F = A’BC’ + AC + AB’

AB=00 F = 10C’ + 0C + 01 = 0AB=01 F = 11C’ + 0C + 00 = C’AB=10 F = 00C’ + 1C + 11 = 1AB=11 F = 01C’ + 1C + 10 = C

Method: evaluate the function for each select input combination…

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ECEn/CS 224

MUXes In A Microprocessor

• They are each 16-bits wide– A 16-bit wide MUX is

simply 16 1-bit wide MUXes

• All with common s inputs

MDR

Memory

MAR

Logic

R0 … R7

PC

zext

zext

+

sext

IR

@+1

Control Logic

N Z P

…

16

16

16

16

1616

1616

16

16

1616 3

3

3

1 1 1

[8:0][5:0]

[7:0]

[8:0]

2

[4:0] 16

16

16

16

16

16

DR

DR

SR2 SR1

selMM

enaMM

enaPC

selPC

ldPC

regWE

regWEldMARldMDR

enaMemOut

regWE

enaALU

ldIR

aluControl

selALUMux

MARMUX PCMUX

ALU

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ECEn/CS 224

Select control lines

bit 0

bit 0

bit 0

16-bit 3:1 MUX Example

00

01

10

11

bit 0

BusA

BusB

BusC

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ECEn/CS 224

BusCBusB

They all use the same select control lines…One bit from each bus goes to each MUX

The result is a 16-bit bus

s1s0

00

01

10

11

bit 0

00

01

10

11

00

01

10

11bi

t 1

bit 1

5

…

BusA

16-bit 3:1 MUX Example

Output

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ECEn/CS 224

Decoders

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ECEn/CS 224

2:4 Decoder

A B Q0 Q1 Q2 Q3

0 0 1 0 0 00 1 0 1 0 01 0 0 0 1 01 1 0 0 0 1

2:4Decode

AB

Q0Q1Q2Q3

Q0 = A’B’ m0 Q1 = A’B m1 Q2 = AB’ m2Q3 = AB m3

A decoder is a minterm generator…

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ECEn/CS 224

3:8 Decoder

A B C Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7

0 0 0 1 0 0 0 0 0 0 00 0 1 0 1 0 0 0 0 0 00 1 0 0 0 1 0 0 0 0 00 1 1 0 0 0 1 0 0 0 01 0 0 0 0 0 0 1 0 0 01 0 1 0 0 0 0 0 1 0 01 1 0 0 0 0 0 0 0 1 01 1 1 0 0 0 0 0 0 0 1

Q0 = A’B’C’ m0 Q1 = A’B’C m1 … …Q7 = ABC m7

3:8Decoder

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ECEn/CS 224

Implementing Logic With Decoders2:4

Decode F = m(0, 2)

2:4Decode F = m(0, 3)

2:4Decode F = M(1, 2)

Historically, some decoders have come with inverted outputs…

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ECEn/CS 224

Uses of Decoders

• Decode 3-bit op-code into a set of 8 signals

op0op1op2

AddSubAndXorNotLoadStoreJump

3:8Decoder

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ECEn/CS 224

ROM: Read-Only Memory

• Can read values from it• Cannot write to it

8 x 1ROM

Add

ress

In

DataOut

Address Data0 11 02 13 04 05 16 17 0

Address Data0 01 72 23 144 265 06 187 22

8 x 5ROM

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ECEn/CS 224

Each minterm of each function can be specified

Read Only Memory (ROM)

3 InputsLines

ABC

F0 F1 F2 F3 F4

5 Outputs Lines

ROM8 wordsx 5 bits

When you program a ROM,you are specifying these

A B C F0 F1 F2 F3 F4

0 0 0 0 0 0 0 10 0 1 0 0 1 1 00 1 0 0 0 1 1 00 1 1 1 0 1 0 11 0 0 0 0 1 1 01 0 1 0 0 1 0 11 1 0 1 0 1 0 11 1 1 1 1 1 1 0

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ECEn/CS 224

ROM – View #1

• An addressable memory– Send in address

(addrn)– Receive data stored

at that location (wn)– Can have multi-bit

data

addr0

addr1

addr2

w4

w3

w2

w1

w0

8 x 5ROM

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ECEn/CS 224

• A hardware implementation of a truth tableROM – View #2

8 x 1ROM

A B C F0 0 0 00 0 1 00 1 0 00 1 1 11 0 0 01 0 1 01 1 0 11 1 1 1

CB

BA

F

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ECEn/CS 224

ROM – Two Different Views

• Both views are accurate

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ECEn/CS 224

ROM Internal Structure

...n InputLines

n:2n

decoder

...

m Output Lines

.

.

.Memory Array

2n words x m bits

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ECEn/CS 224

ROM Memory Array

ABC

m0=A’B’C’m1=A’B’Cm2=A’BC’m3=A’BCm4=AB’C’m5=AB’Cm6=ABC’m7=ABC

F0 F1 F2 F3 F4

F0 = m1 + m4 + m7F1 = m0 + m1 + m2 + m5 …

3:8Decoder

A diode – a one-way ‘resistor’

Resistors – pull outputsdown to GND if no rowwires drive them high0V 0V 0V 0V 0V

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ECEn/CS 224

ROM Technologies: Not Always Diode-Based

• Program Only Once– Mask programmable– Fusible Link

• Re-Programmable– EPROM (ultraviolet erase)– EE-PROM (electrically erase)– Flash memory

Beyond the scope of this class

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ECEn/CS 224

Using a ROM For Logic

F = AB + A’BC’G = A’B’C + C’H = AB’C’ + ABC’ + A’B’C

A B C F G H0 0 00 0 10 1 00 1 11 0 01 0 11 1 01 1 1

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ECEn/CS 224

Using a ROM For Logic

F = AB + A’BC’G = A’B’C + C’H = AB’C’ + ABC’ + A’B’C

A B C F G H0 0 0 00 0 1 00 1 0 10 1 1 01 0 0 01 0 1 01 1 0 11 1 1 1

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ECEn/CS 224

F = AB + A’BC’G = A’B’C + C’H = AB’C’ + ABC’ + A’B’C

Using a ROM For Logic

A B C F G H0 0 0 0 1 00 0 1 0 1 10 1 0 1 1 00 1 1 0 0 01 0 0 0 1 11 0 1 0 0 01 1 0 1 1 11 1 1 1 0 0

Just fill out the truth table

CAD tools usually do the rest…