ECE U322 Digital Logic Design

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ECE U322Digital Logic Design
Oct 3th, 2004

• Lecture 11
• Minimization
• Design of Logic Circuits.
• Modular Combinational Logic
• Multiplexers and Binary Adders
• Reading Marcovitz 5-2, 5-5

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Anouncements

• My office hours
• Monday, 3-4 pm 334 Dana
• Wednesday, 1020-1120 am 334 Dana
• Dont forget TA office hours
• Tuesday, 12 -1 pm 232 Forsyth

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Derivation of the Truth Table

• List all possible input combinations.
• Break circuit into small single-output blocks and
  label.
• Obtain truth table for blocks which depend only
  on input variables.
• Obtain the truth table for blocks with functions
  that depend on previously defined inputs and
  block outputs, until the circuit outputs are
  determined.

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Example Verify the operation of the following
circuit as a binary adder.
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Truth Table
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Design Procedure

• From the specifications, determine the required
  number of inputs and outputs. Assign a symbol to
  each.
• Derive the truth table.
• Obtain the simplified Boolean functions.
• Draw the logic diagram.
• Verify the correctness of the design.

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Example Design a 3-input, 1-output
combinational circuit such that output
logic 1, if binary value of inputs is less
than 011 logic 0, otherwise
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Modular Combinational Logic

• So far
• Start from Boolean equations, simplify then
  implement with logic gates
• Most logic functions occur over and over again
• Design them once
• Put them in a design library
• Reuse them

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Modular Combinational Logic

• Combinational logic designs we will study
• Data selectors (multiplexers)
• Decoders/Encoders
• Demultiplexers
• Binary Arithmetic Circuits
• Adders, Subtractors, Comparators

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Modular Logic Example

• Design a circuit with
• two 4-bit data inputs A and B
• a 2-bit select input s s1s0
• Value of s determines output

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Modular Logic Example

• Implement all functions of A and B in parallel,
  all the time
• Choose the one to go to output based on value of
  s
• A data selector is called a multiplexer

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Datapath for Example circuit
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In Lab 3
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Multiplexers (MUX)

• Data selector.
• Selects binary information from one of many input
  lines to a single output line.
• Selection inputs control which particular input
  line to select.
• Normally, there are 2n input lines, n selection
  inputs, and one output.

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Multiplexers

• A simple multiplexer has a single bit output
• Common Multiplexers are
• 2-to-1 2 inputs __ select lines
• 4-to-1 4 inputs __ select lines
• 8-to-1 8 inputs __ select lines
• 2n-to-1 2n inputs ___select lines

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Example 2-to-1 Multiplexer
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2-to-1 multiplexer

• Y s D0 s D1

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2-to-1 Mux with Enable
E S Y 0 X 0 1 0 D0 1 1
D1
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4 to 1 Multiplexer
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4 2-to-1 muxes
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2 4-to-1 muxes
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In Example

• Choosing one of four different functions of A and
  B
• Each function output is 4 bits wide
• What kind of muxes to use?
• How many?

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Build a 4-to-1 mux out of 2-to-1 muxes
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Arithmetic Circuits

• Combinational circuits that performs arithmetic
  operations such as addition, subtraction,
  multiplication, and division with numbers in a
  binary code.
• We will consider
• adders
• subtracters
• comparators

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Binary Adders

• Addition of two binary digits
• 0 0
• 0 1
• 1 0
• 1 1

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• Half Adder
• Combinational circuit the performs the addition
  of two bits.
• Full Adder
• Combination circuit that performs the addition of
  three bits (two significant bits and a previous
  carry).

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Half Adder
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Full Adder
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