Transcript Chap2-8 (Chap 2-7 in 3 rd ed.)

CS 151
Introduction to Digital Design
Chapter 2-8
Other Gate Types
1
Other Gate Types
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Why?
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Gate classifications
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Implementation feasibility and low cost
Power in implementing Boolean functions
Convenient conceptual representation
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
Primitive gates will be covered first
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Primitive Digital Logic Gates
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Buffer
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A buffer is a gate with the function F = X:
X
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F
In terms of Boolean function, a buffer is the
same as a connection!
So why use it?
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A buffer is an electronic amplifier used to improve
circuit voltage levels and increase the speed of
circuit operation.
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The 3-State Buffer
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For the symbol and truth
Symbol
table, IN is the data input,
OUT
and EN, the control input. IN
For EN = 0, regardless of EN
the value on IN (denoted
Truth Table
by X), the output value is
EN IN OUT
Hi-Z.
0
X
Hi-Z
For EN = 1, the output
1
0
0
value follows the input
1
1
1
value.
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NAND Gate
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The basic NAND gate has the following symbol,
illustrated for three inputs:
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AND-Invert (NAND)
X
Y
Z
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F( X , Y, Z ) = X ×Y ×Z
NAND represents NOT AND, i. e., the AND function
with a NOT applied. The symbol shown is an ANDInvert. The small circle (“bubble”) represents the
invert function.
What does the truth table for NAND look like?
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NAND Gates (continued)
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Applying DeMorgan's Law gives Invert-OR1 (NAND)
X
Y
Z
F( X , Y , Z ) = X + Y + Z
This NAND symbol is called Invert-OR, since inputs are
inverted and then ORed together.
AND-Invert2 and Invert-OR both represent the NAND
gate. Having both makes visualization of circuit function
easier.
A NAND gate with one input degenerates to an inverter.
1.
Also called NOT-OR
2.
Also called AND-NOT
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NAND Gates (continued)
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Universal gate - a gate type that can implement any
Boolean function.
The NAND gate is a universal gate as shown:
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NOR Gate
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The basic NOR gate has the following symbol,
illustrated for three inputs:
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OR-Invert (NOR)
X
Y
Z
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F(X, Y, Z) = X +Y+ Z
NOR represents NOT - OR, i. e., the OR function
with a NOT applied. The symbol shown is an ORInvert. The small circle (“bubble”) represents the
invert function.
What does the truth table for NOR look like?
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NOR Gate (continued)
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Applying DeMorgan's Law gives Invert-AND (NOR)
X
Y
Z
This NOR symbol is called Invert-AND, since inputs
are inverted and then ANDed together.
OR-Invert and Invert-AND both represent the NOR
gate. Having both makes visualization of circuit
function easier.
A NOR gate with one input degenerates to an
inverter.
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NOR Gate (continued)
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The NOR gate is a universal gate
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Complex Digital Logic Gates
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More Complex Gates
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Exclusive OR and Exclusive
NOR gates will be
presented text class.
The remaining complex
gates are SOP or POS
structures with and without
an output inverter.
The names are derived
using:
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A - AND
O - OR
I - Inverter
Numbers of inputs on firstlevel “gates” or directly to
second-level “gates”
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More Complex Gates (continued)
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Example: AOI - AND-OR-Invert
consists of a single gate with
AND functions driving an OR
2-2 AOI
function which is inverted.
Example: 2-2-1 AO has two 2input ANDS driving an OR with
one additional OR input:
2-2 OAI
F = XY + YZ + W
These gate types are used
because:
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the number of transistors
needed is fewer than required
by connecting together
primitive gates
potentially, the circuit delay is
smaller, increasing the circuit
operating speed
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