Combinational Logic: Other Gate Types

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Combinational Logic Other Gate Types
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Gate classifications

• Primitive gate - a gate that can be described
  using a single primitive operation type (AND or
  OR) plus an optional inversion(s).
• Complex gate - a gate that requires more than one
  primitive operation type for its description

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primitive gates

• NAND
• NOR

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NAND Gates
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NOR

• NOT OR
• Also common

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NAND is Universal

• Universal gate Can express any Boolean
  Function using only this type of gate
• Equivalents below

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Sum of Products with NAND

• Easy to think of bubbles as canceling

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AND-OR Circuit Easy to Convert
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NOR Also Universal

• Dual of NAND

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Buffer

• No inversion
• No change, except in power or voltage
• Used to enable driving more inputs

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Parity Function

• How does parity work ?
• Given 7- bit ASCII code for A (100 0001)
• What is the ASCII code for A with even parity ?
• Write truth table for two input even parity
  generator
• What needs to be generated for parity bit?
• What function of two inputs gives you this?
• This is called Exclusive OR function

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Example Complex Digital Logic Gates Exclusive
OR/ Exclusive NOR

• The Exclusive OR (XOR) function is defined as
• The eXclusive NOR (XNOR) function, otherwise
  known as equivalence is

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Symbols For XOR and XNOR

• XOR symbol
• XNOR symbol
• Symbols exist only for two inputs

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Truth Tables for XOR/XNOR

• Operator Rules XOR XNOR
• The XOR function means
• X OR Y, but NOT BOTH
• Why is the XNOR function also known as the
  equivalence function, denoted by the operator ??

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XOR Implementations

• The simple SOP implementation uses the following
  structure
• A NAND only implementation is

X
Y

X
Y
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XOR/XNOR (Continued)

• The XOR function can be extended to 3 or more
  variables. For more than 2 variables, it is
  called an odd function or modulo 2 sum (Mod 2
  sum), not an XOR
• The complement of the odd function is the even
  function.
• The XOR identities

Å
Å


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Question

• Draw the K-map of a 4 variable odd function

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Example Odd Function Implementation

• Design a 3-input odd function F X Y
  Zwith 2-input XOR gates

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Example Odd Function Implementation

• Design a 3-input odd function F X Y
  Zwith 2-input XOR gates
• Factoring, F (X Y) Z

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Example Odd Function Implementation

• Design a 3-input odd function F X Y
  Zwith 2-input XOR gates
• Factoring, F (X Y) Z
• The circuit

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Example Odd Function Implementation

• Design a 3-input odd function F X Y
  Zwith 2-input XOR gates
• Factoring, F (X Y) Z
• The circuit
• Based on the above, given (X,Y,Z,F), then F would
  be the even parity bit for the three bits X,Y,Z.
  Hence, the circuit is an even parity generator.

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Even Parity Generators and Checkers

• An even parity bit could be added to n-bit code
  to produce an n 1 bit code
• Use an odd function to produce codes with even
  parity
• Use odd function circuit to check code words with
  even parity
• Example n 3. Generate even parity code words
  of length 4 withan odd function circuit (parity
  generator)
• Check even parity code words of length 4 with
  odd function circuit
• Operation (X,Y,Z) (0,0,1) gives(X,Y,Z,P)
  (0,0,1,1) and E 0.If Y changes from 0 to 1
  betweengenerator and checker, then E 1
  indicates an error.

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Odd Parity Generators and Checkers

• Similarly, an odd parity bit could be added to
  n-bit code to produce an n 1 bit code
• Use an even function to produce codes with odd
  parity
• Use even function circuit to check code words
  with odd parity

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Tri-State

• Output w/ 3 states H, L, and Hi-Z
• High impedance
• Behaves like no output connection if in Hi-Z (Hi
  Impedance) state
• Allows connecting multiple outputs

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Data Selection

• If s 0, OL IN0, else OL IN1

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Data Selection Function Implementation with
3-State Logic

• Data Selection Function If s 0, OL IN0, else
  OL IN1
• Performing data selection with 3-state buffers
• Since EN0 S and EN1 S, one of the two buffer
  outputs is always Hi-Z plus the last row of the
  table never occurs.

EN0 IN0 EN1 IN1 OL
0 X 1 0 0
0 X 1 1 1
1 0 0 X 0
1 1 0 X 1
0 X 0 X X