1. CSC 220: Computer Organization COMBINATIONAL CIRCUITS-2
College of Computer and Information Sciences
Department of Computer Science
CSC 220: Computer Organization
Unit 6
COMBINATIONAL CIRCUITS-2

2. Unit 6: Combinational Circuits-2 Overview Multiplexers DeMultiplexers Decoders Encoders
Chapter-3
M. Morris Mano, Charles R. Kime and Tom Martin, Logic and Computer Design Fundamentals, Global (5th) Edition, Pearson Education Limited, ISBN:

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13. Implementing Functions with Multiplexers
Prof. Laxmikant Kale - university of illinois at urbana-champaign - Computer Sciences

14. Dr Mohamed A Berbar

15. Demultiplexer
Given an input line and a set of selection lines, the demultiplexer will direct data from input to a selected output line.
An example of a 1-to-4 demultiplexer:
demux
Data D
Outputs
select
S1 S0
Y0 = D.S1'.S0'
Y1 = D.S1'.S0
Y2 = D.S1.S0'
Y3 = D.S1.S0
Demultiplexer 15

16. Demultiplexer
Takes one input
Out to one of 2n possible outputs 16

17. Decoder 17

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21. Decoders with Enable (1/2)
Decoders often come with an enable signal, so that the device is only activated when the enable, E=1.
Truth table: S1 S0
Q0 = ES1'S0'
Q1 = ES1'S0
Q2 = ES1S0'
Q3 = ES1S0 E
Circuit:
Decoders with Enable

22. Demultiplexer Vs Decoder
The demultiplexer is actually identical to a decoder with enable, as illustrated below:
2x4 Decoder D S1 S0
Y0 = D.S1'.S0'
Y1 = D.S1'.S0
Y2 = D.S1.S0'
Y3 = D.S1.S0 E
Exercise: Provide the truth table for above demultiplexer.
Demultiplexer

23. A Demux Using NAND Gates: A Decoder with an Enable23

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26. Dr Mohamed A Berbar 26

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28. Larger Decoders (2/6) 1 1 = enabled 0 = disabled Larger Decoders 3x8w x y 1 : 7
F0 = w'x'y'
F1 = w'x'y
F7 = wxy
2x4
Dec S1 S0 1 2 3
F0 = w'x'y'
F1 = w'x'y
F2 = w'xy'
F3 = w'xy E
F4 = wx'y'
F5 = wx'y
F6 = wxy'
F7 = wxy w x y 1
0 = disabled
1 = enabled
Larger Decoders

29. Larger Decoders (3/6) 1 1 1 = enabled 0 = disabled Larger Decoders 3x8w x y 1 : 7
F0 = w'x'y'
F1 = w'x'y
F7 = wxy
2x4
Dec S1 S0 1 2 3
F0 = w'x'y'
F1 = w'x'y
F2 = w'xy'
F3 = w'xy E
F4 = wx'y'
F5 = wx'y
F6 = wxy'
F7 = wxy w x y 1 1
0 = disabled
1 = enabled
Larger Decoders

30. Larger Decoders (4/6) 1 0 = disabled 1 1 = enabled Larger Decoders 3x8w x y 1 : 7
F0 = w'x'y'
F1 = w'x'y
F7 = wxy
2x4
Dec S1 S0 1 2 3
F0 = w'x'y'
F1 = w'x'y
F2 = w'xy'
F3 = w'xy E
F4 = wx'y'
F5 = wx'y
F6 = wxy'
F7 = wxy w x y 1
1 = enabled
0 = disabled 1
Larger Decoders

31. Larger Decoders (5/6) Question:
4x16
Dec S3 S2 S1 S0 w x y z 1 : 15 F0 F1
F15
Question:
Construct a 4x16 decoder from two 3x8 decoders with 1- enable.
3x8
Dec S2 S1 S0 1 : 7 F0 F1 F7 E F8 F9
F15 w x y z
Larger Decoders

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33. Implementing Functions with Decoder33

34. Dr Mohamed A Berbar 34

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37. Decoders: Implementing Functions Example: Full addery z 1 2 3 4 5 6 7 S C 1
Decoders: Implementing Functions
CS1104-7

38. Decoders: Implementing Functions
3x8
Dec S2 S1 S0 x y z 1 2 3 4 5 6 7 S C 1 1 1
Decoders: Implementing Functions
CS1104-7

39. Using a 38 decoder (assuming 1-enable and active-high outputs).
Example:
F(a,b,c) =  m(4,6,7)
Using a 38 decoder (assuming 1-enable and active-high outputs).
3x8
Dec S2 S1 S0 a b c 1 2 3 4 5 6 7 F EN
Reducing Decoders
CS1104-7

40. Encoder Encoder is the opposite of decoder
2n inputs or less and n outputs
Example: Decimal to BCD
10 inputs : I0, I1, I2, I3, …, I9
4 output lines 40

41. Example: Designing an Octal to binary Encoder
Example: Designing an Octal to binary Encoder Inputs: 8 (D7 … D0) Outputs: 3 (A2 … A0) Truth Table: 41

42. Inputs are Minterms
Can OR the minterms appropriately to get each of the outputs A0, A1, A2
Example: A0 = D1 + D3 + D5 + D7 42

43. Generating Outputs using OR of Minterms
A0 = D1 + D3 + D5 + D7
A1 = D2 + D3 + D6 + D7
A2 = D4 + D5 + D6 + D7 43