Multiplexors

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Multiplexors
Lecture 6

• And Decoders
• Prof. Sin-Min Lee
• Department of Computer Science

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Two-Level NAND Gate Implementation

Example 1  
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Two-Level NAND Gate Implementation
Example 1  

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Design Procedure

• Determine the required number of inputs and
  outputs and assign letter symbols to them.
• Derive the truth table that defines the required
  relationship between inputs and outputs.
• Obtain the Boolean function.
• Draw the logic diagram.
• Verify the correctness of the design.

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Example

• Design a circuit that converts a BCD codeword to
  its corresponding excess-3 codeword. We need 4
  input variables and 4 output variables. Let us
  designate the 4 input binary variables by the
  symbols A, B, and C and D, and the four output
  variables by w, x, y, and z. The truth table
  relating the input and output variables is shown
  below

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Note that the outputs for inputs 1010 through
1111 are don't care.
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Two-Lvel NOR Gate Implementation
Example 2  
e

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Richard Hamming Richard Wesley Hamming,
mathematician, pioneer computer scientist, and
professor, died of a heart attack on January 7,
1998, in Monterey, California, at the age of 82.
His research career began at Bell Laboratories in
the 1940s, in the early days of electronic
computers, and included the invention of the
Hamming error-correcting codes. In the 1970s he
shifted to teaching, and at his death he was
Distinguished Professor Emeritus of computer
science at the Naval Postgraduate School. He is
survived by his wife Wanda, a niece, and a
nephew.
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1948 Error Correction Error-detecting coding,
first developed for telephone switching, is now
used throughout the computing and
telecommunications industries. In 1948 , R.W.
Hamming (left) of Bell Labs developed a general
theory for error-correcting schemes in which
"check-bits" are interspersed with information
bits to form binary words in patterns. When a
single error occurs in transmission, the word
becomes invalid, but the error is automatically
located and corrected.
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Multiplexers

• A combinational circuit that selects info from
  one of many input lines and directs it to the
  output line.
• The selection of the input line is controlled by
  input variables called selection inputs.
• They are commonly abbreviated as MUX.

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Combinational circuit implementation using MUX

• We can use Multiplexers to express Boolean
  functions also.
• Expressing Boolean functions as MUXs is more
  efficient than as decoders.
• First n-1 variables of the function used as
  selection inputs last variable used as data
  inputs.
• If last variable is called Z, then each data
  input has to be Z, Z, 0, or 1.

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Karnaugh Map Method of Multiplexer Implementation
Consider the function
A is taken to be the data variable and B,C to be
the select variables.
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Example of MUX combo circuit

• F(X,Y,Z) Sm(1,2,6,7)

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