Combinational circuits ,encoder,decoder, Slides of Digital Logic Design and Programming

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Combinational Logic

Part 2

Outline

1. Combinational Circuits

2. Analysis Procedure

3. Design Procedure

4. Magnitude Comparator

5. Binary Adder-Subtractor

6. Decimal Adder

7. Binary Multiplier

8. Decoders

9. Encoders

10. Multiplexers

Truth table of 3-to-8 line decoder

Logic implementation of 3 - to-

8 line decoder

2 - to- 4 line Decoder

4X16 Decoder Constructed

with 3X8 Decoders

8

Full Adder Implementation

with Decoders and OR Gates

◼ S = ∑(1, 2, 4, 7) ◼ C = ∑(3, 5, 6, 7)

Encoders

◼ Encoders perform the inverse operation of decoders ◼ 2 n input to n output

Problem of Regular Encoder

• One of the main disadvantages of standard digital encoders is that they can generate the wrong output code when there is more than one input present at logic level “ 1 ”. For example, if we make inputs D 1 and D 2 HIGH at logic “ 1 ” both at the same time, the resulting output is neither at “ 01 ” or at “ 10 ” but will be at “ 11 ” which is an output binary number that is different to the actual input present. Also, an output code of all logic “ 0 ”s can be generated when all of its inputs are at “ 0 ” OR when input D 0 is equal to one.
• One simple way to overcome this problem is to “Prioritise” the level of each input pin. So if there is more than one input at logic level “ 1 ” at the same time, the actual output code would only correspond to the input with the highest designated priority. Then this type of digital encoder is known commonly as a Priority Encoder or P- encoder for short.

Priority Encoder

x = D

2

+ D

3

y = D 3 + D 1 D 2 ’

V = D

0

+ D

1

+ D

2

+ D

3

Logic Implementation of

Priority Encoder

8X3 Priority Encoder

Applications: Positional Encoder Another more common application is in magnetic positional control as used on ships navigation or for robotic arm positioning etc. Here for example, the angular or rotary position of a compass is converted into a digital code by a 74 LS 148 8 - to- 3 line priority encoder and input to the systems computer to provide navigational data and an example of a simple 8 position to 3 - bit output compass encoder is shown below. Magnets and reed switches could be used at each compass point to indicate the needles angular position.

Multiplexer

◼ Multiplexer selects binary information form one of many input lines and detects it to a single output line. ◼ 2 n input and n selection lines to 1 output