Combinational Logic Design-Digital Logic Design-Lecture Slides, Slides of Digital Logic Design and Programming

Prof. Sourabhi Kapoor delivered this course at Bengal Engineering and Science University. This lecture covers following points for Digital Logic Design course: Digital, System, Combinational, Logic, Procedure, Decoder, Encoder, Converters, Binary, Priority

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2011/2012

Uploaded on 07/30/2012

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EE207: Digital Systems I, Semester I
2003/2004
CHAPTER 3 -ii:
Combinational Logic Design
Design Procedure, Encoders/Decoders
(Sections 3.4 3.6)
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Download Combinational Logic Design-Digital Logic Design-Lecture Slides and more Slides Digital Logic Design and Programming in PDF only on Docsity!

EE207: Digital Systems I, Semester I

CHAPTER 3 -ii:

Combinational Logic Design –

Design Procedure, Encoders/Decoders

(Sections 3.4 – 3.6)

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Overview

  • Design Procedure
  • Code Converters
  • Binary Decoders
    • Expansion
    • Circuit implementation
  • Binary Encoders
  • Priority Encoders

18-Jul-12 Chapter 3-ii: Combinational Logic Design (3.4 - 3.6) 2 docsity.com

Design Procedure

  1. Determine the required number of inputs and outputs and assign variables to them.
  2. Derive the truth table that defines the required relationship between inputs and outputs.
  3. Obtain and simplify the Boolean function (K-maps, algebraic manipulation, CAD tools, …). Consider any design constraints (area, delay, power, available libraries, etc).
  4. Draw the logic diagram.
  5. Verify the correctness of the design.

18-Jul-12 Chapter 3-ii: Combinational LogicDesign (3.4 - 3.6) (^) docsity.com 4

Design Example

  • Design a combinational circuit with 4 inputs

that generates a 1 when the # of 1s equals the

# of 0s. Use only 2-input NOR gates

18-Jul-12 Chapter 3-ii: Combinational LogicDesign (3.4 - 3.6) (^) docsity.com 5

BCD-to-Excess-3 Code Converter

  • Design a circuit that converts a binary-coded- decimal (BCD) codeword to its corresponding excess-3 codeword.
  • Excess-3 code: Given a decimal digit n , its corresponding excess-3 codeword (n+3) 2 Example: n=5  n+3=8  (^1000) excess- n=0  n+3=3  (^0011) excess-
  • We need 4 input variables (A,B,C,D) and 4 output functions W(A,B,C,D), X(A,B,C,D), Y(A,B,C,D), and Z(A,B,C,D).

18-Jul-12 Chapter 3-ii: Combinational LogicDesign (3.4 - 3.6) (^) docsity.com 7

BCD-to-Excess-3 Converter (cont.)

  • The truth table relating the input and output variables is shown below.
  • Note that the outputs for inputs 1010 through 1111 are don't care s (not shown here).

18-Jul-12 Chapter 3-ii: Combinational Logic Design (3.4 - 3.6) 8 docsity.com

BCD-to-Excess-3 Converter (cont.)

18-Jul-12 Chapter 3-ii: Combinational LogicDesign (3.4 - 3.6) (^) docsity.com 10

Another Code Converter Example:

BCD-to-Seven-Segment Converter

  • Seven-segment display:
    • 7 LEDs (light emitting diodes), each one controlled by an input
    • 1 means “on”, 0 means “off”
    • Display digit “3”?
      • Set a, b, c, d, g to 1
      • Set e, f to 0

18-Jul-12 Chapter 3-ii: Combinational Logic Design (3.4 - 3.6) 11

d

a

b

e c

f g

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BCD-to-Seven-Segment (cont.)

Truth Table

18-Jul-12 Chapter 3-ii: Combinational LogicDesign (3.4 - 3.6) 13

Digit wxyz abcdefg

0 0000 1111110 1 0001 0110000 2 0010 1101101 3 0011 1111001 4 0100 0110011 5 0101 1011011 6 0110 X 7 0111 11100X

Digit wxyz abcdefg 8 1000 1111111 9 1001 111X 1010 XXXXXXX 1011 XXXXXXX 1100 XXXXXXX 1101 XXXXXXX 1110 XXXXXXX 1111 XXXXXXX

??

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Decoders

  • A combinational circuit that converts binary

information from n coded inputs to a

maximum 2 n^ decoded outputs

 n-to- 2 n^ decoder

• n-to-m decoder, m ≤ 2 n

  • Examples: BCD-to-7-segment decoder, where

n=4 and m=

18-Jul-12 Chapter 3-ii: Combinational LogicDesign (3.4 - 3.6) (^) docsity.com 14

18-Jul-12 Chapter 3-ii: Combinational LogicDesign (3.4 - 3.6) 16

2-to-4 Decoder

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18-Jul-12 Chapter 3-ii: Combinational LogicDesign (3.4 - 3.6) 17

2-to-4 Active Low Decoder

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3-to-8 Decoder (cont.)

  • Three inputs, A 0 , A 1 , A 2 , are decoded into eight

outputs, D 0 through D 7

  • Each output D i represents one of the minterms of the

3 input variables.

  • D i = 1 when the binary number A 2 A 1 A 0 = i
  • Shorthand: D i = m i
  • The output variables are mutually exclusive ; exactly

one output has the value 1 at any time, and the other seven are 0.

18-Jul-12 Chapter 3-ii: Combinational LogicDesign (3.4 - 3.6) (^) docsity.com 19