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CS 140 Lecture 12 Standard Combinational Modules. Professor CK Cheng CSE Dept. UC San Diego. Part III - Standard Combinational Modules. Decoder: Decode address Encoder: Encode address Multiplexer (Mux): Select data by address Demultiplexier (DeMux): Direct data by address

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cs 140 lecture 12 standard combinational modules

CS 140 Lecture 12Standard Combinational Modules

Professor CK Cheng

CSE Dept.

UC San Diego

part iii standard combinational modules
Part III - Standard Combinational Modules
  • Decoder: Decode address
  • Encoder: Encode address
  • Multiplexer (Mux): Select data by address
  • Demultiplexier (DeMux): Direct data by address
  • Shifter: Shift bit location
  • Adder: Add two binary numbers
  • Multiplier: Multiply two binary numbers
interconnect decoder encoder mux demux

Arbiter

Data 1

P1

Mux,

Memory Bank

Data

Address 1

P2

Demux

n-m

Mux

Address 2

Address

n

m

2m

Address k

Decoder

Data k

Pk

Interconnect: Decoder, Encoder, Mux, DeMux
1 decoder
1. Decoder
  • Definition
  • Logic Diagram
  • Application (Universal Set)
  • Tree of Decoders
slide5

1. Decoder: Definition

EN (enable)

y0

y1

y7

0

1

2

3

4

5

6

7

I0

0

.

.

1

I1

I2

2

n to 2n decoderfunction:

2n outputs

23= 8

n inputs

n= 3

yi = 1 if En= 1 & (I2, I1, I0 ) = i

yi= 0 otherwise

1 decoder definition
1. Decoder: Definition
  • N inputs, 2N outputs
  • One-hot outputs: only one output HIGH at once
slide7

Decoder: Logic Diagram

yi = mi En

En

y0 = 1 if (I2, I1, I0 ) = (0,0,0) & En = 1

I0’

I1’

y0

I2’

I0’

I1’

y1

I2

.

.

I0

y7 = I2I1I0En

I1

y7

I2

slide8

En

y0

y1

.

.

y7

0

1

2

3

4

5

6

7

c

I0

I1

b

a

I2

Decoder Application: universal set {Decoder, OR}

Implement functions f1(a,b,c) = Sm(1,2,4)

Example:

f2(a,b,c) = Sm(2,3), and

f3(a,b,c) = Sm(0,5,6)

with a 3-input decoder and OR gates.

y1

y2

y4

f1

y2

y3

f2

y0

y5

y6

f3

decoders
Decoders
  • OR minterms
slide10

Tree of Decoders

Implement a 4-24 decoder with 3-23 decoders.

y0

y1

y7

0

1

2

3

4

5

6

7

d

I0

c

I1

b

I2

y8

y9

y15

0

1

2

3

4

5

6

7

I0

I1

I2

a

slide11

Tree of Decoders

Implement a 6-26 decoder with 3-23 decoders.

En

En

y0

D0

I2, I1, I0

y7

y8

I5, I4, I3

D1

I2, I1, I0

y15

y56

D7

I2, I1, I0

y63

2 encoder
2. Encoder
  • Definition
  • Logic Diagram
  • Priority Encoder
slide13

2. Encoder: Definition

En

I2n-1…I0

yn-1 …y0

A

Encoder Description:

En

At most one Ii = 1.

(yn-1,.., y0 ) = i if Ii = 1 & En = 1

(yn-1,.., y0 ) = 0 otherwise.

A = 1 if En = 1 and one i s.t. Ii = 1

A = 0 otherwise.

I0

0

1

2

3

4

5

6

7

y0

0

1

2

y1

y2

I7

3 outputs

A

8 inputs

slide14

Encoder: Logic Diagram

En

y0

I1

I3

I5

I7

En

y1

I2

I3

I6

I7

slide15

Encoder: Logic Diagram

En

y2

I4

I5

I6

I7

En

A

I0

I1

.

.

I6

I7

slide16

Priority Encoder: Definition

Description: Input (I2n-1,…, I0), Output (yn-1 ,…,,y0)

(yn-1 ,…,,y0) = i if Ii = 1 & En = 1 & Ik = 0

for all k > i (high bit priority) or

for all k< i (low bit priority).

Eo = 1 if En = 1 & Ii = 0 for all i,

Gs = 1 if En = 1 & i s.t. Ii = 1.

En

E

(Gs is like A, and Eo tells us if enable is true or not).

I0

0

1

2

3

4

5

6

7

y0

0

1

2

y1

y2

I7

Eo

Gs

slide17

Priority Encoder: Implement a 32-input priority encoder w/ 8 input priority encoders (high bit priority).

En

I31-24

y32, y31, y30

Gs

Eo

I25-16

y22, y21, y20

Gs

Eo

I15-8

y12, y11, y10

Gs

Eo

I7-0

y02, y01, y00

Gs

Eo