logic gates. outline logic gates the inverter the and gate the or gate the nand gate the nor...
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Logic Gates
Outline
Logic Gates The Inverter The AND Gate The OR Gate The NAND Gate The NOR Gate The XOR Gate The XNOR Gate
Drawing Logic Circuit Analysing Logic Circuit
Outline
Logic Gates The Inverter The AND Gate The OR Gate The NAND Gate The NOR Gate The XOR Gate The XNOR Gate
Drawing Logic Circuit Analysing Logic Circuit
Logic Gates Gate Symbols
EXCLUSIVE OR
a
ba.b
a
ba+b
a a'
a
b(a+b)'
a
b(a.b)'
a
ba b
a
ba.b&
a
ba+b1
AND
a a'1
a
b(a.b)'&
a
b(a+b)'1
a
ba b=1
OR
NOT
NAND
NOR
Symbol set 1 Symbol set 2
(ANSI/IEEE Standard 91-1984)
Logic Gates: The Inverter
The Inverter
A A'
0 1 1 0
A A' A A'
Application of the inverter: Complement.
1
0
0
1
0
1
0
1
1
0
0
1
1
0
1
0
Binary number
1’s Complement
Logic Gates: The AND Gate (1/2)
The AND Gate
A B A . B0 0 00 1 01 0 01 1 1
A
BA.B
&A
BA.B
Logic Gates: The AND Gate (2/2)
Application of the AND Gate
1 sec
A
1 secEnable
A
EnableCounter
Reset to zero between Enable pulses
Register, decode and frequency display
Logic Gates: The OR Gate
The OR Gate
1
A
BA+B
A
BA+B
A B A + B0 0 00 1 11 0 11 1 1
Logic Gates: The NAND Gate
The NAND Gate
&A
B(A.B)'
A
B(A.B)'
A
B(A.B)'
NAND Negative-OR
A B (A.B)'0 0 10 1 11 0 11 1 0
Logic Gates: The NOR Gate
The NOR Gate
NOR Negative-AND
1
A
B(A+B)'A
B(A+B)'
A
B(A+B)'
A B (A+B)'0 0 10 1 01 0 01 1 0
Logic Gates: The XOR Gate
The XOR Gate
=1A
BA B
A
BA B
A B A B0 0 00 1 11 0 11 1 0
Logic Gates: The XNOR Gate
The XNOR Gate
A
B(A B)'
=1A
B(A B)'
A B (A B) '0 0 10 1 01 0 01 1 1
Outline
Logic Gates The Inverter The AND Gate The OR Gate The NAND Gate The NOR Gate The XOR Gate The XNOR Gate
Drawing Logic Circuit Analysing Logic Circuit
Drawing Logic Circuit (1/2)
When a Boolean expression is provided, we can easily draw the logic circuit.
Examples:
(i) F1 = x.y.z' (note the use of a 3-input AND gate)
xy
z
F1
z'
Drawing Logic Circuit (2/2)
(ii) F2 = x + y'.z (if we assume that variables and their complements are available)
(iii) F3 = x.y' + x'.z
x
y'z
F2
y'.z
x'z
F3
x'.z
x.y'xy'
Outline
Logic Gates The Inverter The AND Gate The OR Gate The NAND Gate The NOR Gate The XOR Gate The XNOR Gate
Drawing Logic Circuit Analysing Logic Circuit
Analysing Logic Circuit
When a logic circuit is provided, we can analyse the circuit to obtain the logic expression.
Example: What is the Boolean expression of F4?
A'.B'
A'.B'+C (A'.B'+C)'
A'
B'
CF4
F4 = (A'.B'+C)' = (A+B).C'