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EMT 125/3
DIGITAL ELECTRONIC PRINCIPLES

COMBINATIONAL LOGIC
FUNCTIONS

SITI ZARINA BINTI MD NAZIRI | SCHOOL OF MICROELECTRONIC ENGINEERING | UniMAP

Dr
...
edu
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Norina
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Encoder
 Encoders typically have 2N inputs and N outputs
...

 Typical examples include:
4–to–2 encoders (probably not used much)
8–to–3 encoders
16–to–4 encoders

Encoder
 Review of simple binary codes:

Remember the
4-bit codes?

Encoder
Example:
8-to-3 Binary Encoder

0

Truth table

Logic Diagram

Remember: Only one of the inputs can be 1!
9

Encoder
Example
Decimal to BCD (10-to-4) Encoder

Your task:

DESIGN!

10

Encoder
Example
Design a Decimal to BCD Encoder

Hints:

(a) Draw a Truth-Table showing input and output
- How many inputs?
: 10 (0 to 9)
- How many outputs?
: 4 because we need 4 bits to express 9 (1001)
(b) From the Truth-Table, get the equation for each
output
- How many Boolean expression?
: 4 since there are 4 outputs
(c) Based on the output equation, draw a circuit for
basic decimal-to-BCD encoder

Encoder
Draw a Truth-Table showing input and output
DECIMAL
DIGIT

BCD CODE
A3

A2

A1

A0

0

0

0

0

0

1

0

0

0

1

2

0

0

1

0

3

0

0

1

1

4

0

1

0

0

5

0

1

0

1

6

0

1

1

0

7

0

1

1

1

8

1

0

0

0

9

1

0

0

1

Encoder
(b) From the Truth-Table, get the
equation for each output:
A3=
A2=
A1=
A0=

Σ
Σ
Σ
Σ

m(8,
m(4,
m(2,
m(1,

(a)

9)
5, 6, 7)
3, 6, 7)
3, 5, 7, 9)

(c) Based on the output
equation, draw a circuit for
basic decimal-to-BCD encoder
(a) Logic symbol for a 10-line-to 4
line encoder
(b) Logic diagram
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Example:
D3 = D6 = 1

Output = 0110
(D6 has a higher priority than D3)
14

Priority Encoder
 If 2 or more inputs are equal to 1 at the same

time, the input having the highest priority is the
one encoded
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 V (valid) =1 when 1 or more input is equal to 1
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Do the opposite of encoder

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Decoders

 Decoders are the opposite of decoders
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 Typical examples include:
2–to–4 decoders
3–to–8 decoders
4–to–16 decoders

Decoders
 Decoders come in two varieties:
- active high
- active low

 We focus our lectures on active high decoders:
- the selected output goes to logic 1
- the outputs not selected stay at logic 0
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 AND gate -> produce HIGH output when all inputs are HIGH
 How to ensure that inputs to the AND gate are HIGH when
binary 1001 occurs?

Other than this input
combinations, the
output is 0

Decoding logic for the binary code 1001 with an active-HIGH output
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A4
A3
A2

Active-HIGH  produce HIGH output

A1

Decoding function,

A0

Decodingfu nction , X  A4 A3 A2 A1 A0

Decoder
3 to 8
Binary
Decoder

The inputs are treated as a binary number and the output selected is made active
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(b) From the Truth-Table, get the equation for
each output
...

Same steps used to design
an encoder!

Decoder
4-line-to-16-line Decoder

Draw the truth-table for
this decoder

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Decoder
The BCD to Decimal Decoder

Draw the truth-table for
this decoder

30

Decoder
The BCD to 7 Segment Decoder
 Accepts BCD code on inputs and provide outputs to drive
7-segment display devices to produce a decimal readout
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Display of decimal digits with a 7-segment device
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Requires logic
0 to light up
(ON) a segment
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Decoder
Seven Segment Decoder

Block diagram of 7-segment logic and display
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 Derive an SOP for segment a
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 Draw the logic circuit to implement segment a of
the 7-segment display
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Design Example

The minimum logic implementation for segment a of the 7-segment display

Decoders – Fn Implementation
Example:
Implementing a Binary Adder Using a Decoder

For an addition of X, Y, and Z (as Cin), the S and
Cout expression are as follows:
S(X,Y,Z) = m (1, 2, 4, 7)
C(X,Y,Z) = m (3, 5, 6, 7)

So, there are 3 inputs and 8 minterms
 Use a 3-to-8 decoder
...
e
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Decoders - Expansion
Example:

A 3-to-8 Decoder Constructed with Two 2-to-4 Decoders

Decoder - Expansion
 Truth Table:

Decoders - Expansion
The Operation
The MSB input, A2, functions:
 As enable, EN, of one decoder
 As its complement, EN to the other decoder
When A2=0,
 Top decoder enabled  Generates minterms D0 to
D3
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When A2=1,
 Top decoder disabled  Outputs equal to 0
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Decoders - Expansion
The function of EN input

 Very useful and convenient way to interconnect


2 or more functional blocks
For the purpose of expanding digital functions
into:
 Similar functions with more inputs and
outputs
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…
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