7/28/2019 Crossbar Swtich Theory

1/17

ELE2120 Digital Circuits and Systems

Tutorial Note 6

7/28/2019 Crossbar Swtich Theory

2/17

Outline

1. Crossbar switch

2. Decoder

4. De-multiplexer

3. Encoder & Code converter

5. Code converter

7/28/2019 Crossbar Swtich Theory

3/17

Crossbar switch

N x Kcrossbar swi tch:A circuit that has N inputs and K outputs, whose

sole function is to provide a capability to connect any input to any output.

2x 2 crossbar switch

Applications: to be able to connect one set of switches to another set of

wires, where the connection pattern changes from time to time. Telephony

crossbar switch, mechanical sorting machines with inputs, etc.

7/28/2019 Crossbar Swtich Theory

4/17

Crossbar switch

Circuit built by multiplexers

s y1 y2

0 x1 x2

1 x2 x1

Truth table

7/28/2019 Crossbar Swtich Theory

5/17

Decoder

Decoder circuits are used to decode encoded information. A

binary decoder, depicted below is a logic circuit with n inputs

and 2 outputs

When En=1, the pattern of the input determines which one of the outputs

is asserted, otherwise, none of the output is asserted.

7/28/2019 Crossbar Swtich Theory

6/17

Decoder

One-hot encoded: only one input is asserted each time.

(a) Graphical symbol (b) Truth table

A 2-to-4 decoder is given below:

7/28/2019 Crossbar Swtich Theory

7/17

Decoder

(c) Circuit Diagram

Steps for implementing decoder circuit diagram

(a) Graphical symbol

1. Identify input and output

number.2. Draw the truth table.

3. # of Output = # of AND gate

4. # of Input + 1 = # of input of

AND gate.

5. From Truth table, find out the

function for each output.

6. Implement the logic function.

7/28/2019 Crossbar Swtich Theory

8/17

Decoder

Larger decoders can be built by smaller decoders.

Example: two 2-to-4 decoders to build a 3-to-8 decoder

Extra part

added to

extract the

input

number

7/28/2019 Crossbar Swtich Theory

9/17

De-multiplexer

A circuit that performs the opposite function of a multiplexer, namely, placing the

value of a single data input onto multiple data outputs, is called a de-multiplexer.

The de-multiplexer can be implemented using a decoder circuit.

For example, 2-to-4 decoder can be used as a 1-to-4 de-multiplexer.

En y0 y1 y2 y3

0 0 0 0 0

1 w0w1 w0w1 w0w1 w0w1

1.Input of decoder: except En; Input of de-multiplexer: En only.

2.Output of decoder = output of the de-multiplexer.

7/28/2019 Crossbar Swtich Theory

10/17

Encoder

A binary encoder encodes information from 2 inputs into an n-bit code, as

indicated below.

Exactly one of the input signals should have a value of 1, and the outputs

present the binary number that identifies which input is equal to 1.

(a) A 2 inputs into an n-bit encoder (b) Truth table for the encoder

7/28/2019 Crossbar Swtich Theory

11/17

Encoder

Encoders are used to reduce the number of bits needed to represent

given information.

Application: encoders is for transmitting information in a digital system.

(c) Circuit for the encoder(b) Truth table for the encoder

7/28/2019 Crossbar Swtich Theory

12/17

Code converter

BCD-to-7 segment converter, which converts one binary coded decimal

into information suitable for driving 1 digit-oriented display.

LED (Light Emitting

Diode)

Code converter

7/28/2019 Crossbar Swtich Theory

13/17

Code converter

w3 w2 w1 w0 a b c d e f g

0 0 0 0 1 1 1 1 1 1 0

0 0 0 1 0 1 1 0 0 0 0

0 0 1 0 1 1 0 1 1 0 1

0 0 1 1 1 1 1 1 0 0 1

0 1 0 0 0 1 1 0 0 1 1

0 1 0 1 1 0 1 1 0 1 1

0 1 1 0 1 0 1 1 1 1 1

0 1 1 1 1 1 1 0 0 0 0

1 0 0 0 1 1 1 1 1 1 1

1 0 0 1 1 1 1 1 0 1 1

Truth Table for BCD-to-7

7/28/2019 Crossbar Swtich Theory

14/17

Exercise: Code Converter

Design a octal-to-binary code converter. (2 to n --- encoder)

Step I: Identify the input and output

D0

D1

D2

D3

D4

D5

D6

D7

A0

A1

A2

7/28/2019 Crossbar Swtich Theory

15/17

Exercise: Code Converter

Step II: truth table

D7 D6 D5 D4 D3 D2 D1 D0 A2 A1 A0

0 0 0 0 0 0 0 1 0 0 0

0 0 0 0 0 0 1 0 0 0 10 0 0 0 0 1 0 0 0 1 0

0 0 0 0 1 0 0 0 0 1 1

0 0 0 1 0 0 0 0 1 0 0

0 0 1 0 0 0 0 0 1 0 1

0 1 0 0 0 0 0 0 1 1 0

1 0 0 0 0 0 0 0 1 1 1

OutputInput

7/28/2019 Crossbar Swtich Theory

16/17

Exercise: Code Converter

Step III: Function representation

D7 D6 D5 D4 D3 D2 D1 D0 A2 A1 A0

0 0 0 0 0 0 0 1 0 0 0

0 0 0 0 0 0 1 0 0 0 10 0 0 0 0 1 0 0 0 1 0

0 0 0 0 1 0 0 0 0 1 1

0 0 0 1 0 0 0 0 1 0 0

0 0 1 0 0 0 0 0 1 0 1

0 1 0 0 0 0 0 0 1 1 0

1 0 0 0 0 0 0 0 1 1 1

A2=D4+D5+D6+D7

A1=D2+D3+D6+D7

A0=D1+D3+D5+D7

7/28/2019 Crossbar Swtich Theory

17/17

Exercise: Code Converter

Step IV: Circuit diagram