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EE2420 – Digital LogicSummer II 2013

Set 12: Multiplexers, Decoders,

Encoders, Shift Register

Class book: Chapter 6

Online book: chapter 8

Hassan Salamy

Ingram School of Engineering

Texas State University

Multiplexer

- In its standard form, a multiplexer takes an N-bit control input to determine which of 2N data inputs will be passed to its single output.
- In other words, a multiplexer selects one of multiple inputs
- Functions may be implemented by using a combination of the control inputs and data inputs.

A 2-to-1 multiplexer

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(b) Truth table

(a) Graphical symbol

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(c) Sum-of-products circuit

A 4-to-1 multiplexer.

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(a) Graphic symbol

(b) Truth table

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(c) Circuit

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A practical application of multiplexers

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(a) A 2x2 crossbar switch

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(b) Implementation using multiplexers

Synthesis of a logic function using multiplexers

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(a) Implementation using a 4-to-1 multiplexer

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(c) Circuit

(b) Modified truth table

Implementation of the three-input majority function using a 4-to-1 multiplexer.

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(a) Modified truth table

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(b) Circuit

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Three-input XOR implemented wit 2-to-1 multiplexers

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(a) Truth table

(b) Circuit

Three-input XOR function implemented with a 4-to-1 multiplexer

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(b) Circuit

(a) Truth table

The three-input majority function implemented using a 2-to-1 multiplexer.

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(b) Truth table

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(b) Circuit

What is a Demultiplexer (DEMUX)?

Demultiplexer

Block Diagram

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DEMUX

- A DEMUX is a digital switch with a single input (source) and a multiple outputs (destinations).
- The select lines determine which output the input is connected to.
- DEMUX Types

1-to-2 (1 select line)

1-to-4 (2 select lines)

1-to-8 (3 select lines)

1-to-16 (4 select lines)

Typical Application of a DEMUX

Multiple Destinations

Single Source

Selector

B/W Laser

Printer

Fax

Machine

Color Inkjet

Printer

D0

D1

D2

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Pen

Plotter

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DEMUX

Decoder

- In its standard form, a decoder takes an N-bit input and outputs 2N functions, each of which is active for exactly one input combination.
- In other words, a decoder outputs the minterms of the inputs (or with inverted outputs, the maxterms)
- Functions may be implemented with the addition of a single extra gate. For example, an OR gate may be used to combine minterms for a sum-of-products implementation or an AND gate may be used to combine maxterms for a product-of-sums implementation.

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(a) Truth table

(b) Graphical symbol

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(c) Logic circuit

A 2-to-4 decoder.

A 3-to-8 decoder using two 2-to-4 decoders.

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A 4-to-16 decoder built using a decoder tree.

Decoders: Designing Logic Circuits

F = Sm(0,2)

A 2m x n read-only memory (ROM) block.

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A 4-to-2 binary encoder.

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(a) Truth table

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4-bit Data Shifter

- Data Shifter
- A combinational logic shifter is a device that produces an output obtained by shifting its input
- Right Shift: The Most Significant bit is called the fill bit and the Least Significant bit is called the spill bit
- Left Shift: MSB is the spill bit – LSB is the fill bit
- Processes:
- Logical Shift => a logic zero is inserted in the fill position
- Arithmetic => the sign bit is extended in a right shift
- End-around [or rotate]

4-bit Logical ShifterProblem Statement

- Step 1: Clear Problem Statement
- Design and implement a 4-bit logical shifter that has 4-bit input “A”, 4-bit output “S”, and 1-bit controls X and Y where:

4-bit Logical ShifterConceptualization

- Step 2: Conceptualization
- This 4-bit shifter can be represented by the black-box model below with the associated Output Table

4-bit Logical Shifter Solution/Simplification

- Step 3: Solution/Simplification
- The output table, with it’s different terms and exact duplication of bit values - - Should suggest a multiplexer
- The logic functions describing the assignment of the values is:

4-bit Logical Shifter Realization and Verification

- Step 4: Realization
- Those 4 output values can be implemented using four 4-to-1 mux’s as follows:
- Step 5: Verification
- Lab time! - - Does it really do what you designed it to do?
- Return to that K-map/Truth table and be sure!

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