logic gates shashidhara h s dept. of ise msrit. basic logic design and boolean algebra gates = basic...
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Logic Gates
Shashidhara H S
Dept. of ISE
MSRIT
Basic Logic Design and Boolean Algebra
GATES = basic digital building blocks which correspond to and perform the basic logical functions. The three fundamental gates are:
AND: Is a logical product . Its output = 1, only if both inputs are 1.
Boolean Expression: A • B “product”
Logic Gate:
Truth Table:
Complex digital functions that make up a computer are built from these basic digital building blocks
A
B C
A B C
0 0 0
0 1 0
1 0 0
1 1 1
Basic Logic Design and Boolean Algebra
· OR: Is a logical sum. Its output = 1 if either input = 1.
Boolean Expression: A + B , “sum”
Logic Gate:
Truth Table:
A
B
C
A B C
0 0 0
0 1 1
1 0 1
1 1 1
Basic Logic Design and Boolean Algebra
NOT: Is a logical inversion since its output is opposite of its input. __ Boolean Expression: A or ~A , “not”
Logic Gate:
Truth Table
A ~A
0 1
1 0
AA
_
Laws of Boolean Algebra Identity law: A + 0 = A and A • 1 = A Zero and One laws: A + 1 = 1 and A • 0 = 0 Inverse Laws: A + A = 1and A • A = 0 Commutative laws: A + B = B + A and A • B = B • A
Associative laws: A + (B + C) = (A + B) + C and A • (B • C) = (A • B) • C
Distributive laws: A • (B + C) = (A • B) + (A • C) and A + (B • C) = (A + B) • (A + C) _____ __ __ De Morgan’s laws: (A + B) = (A) • (B) and _____ __ __ (A • B) = (A) + (B)
More Logic Gates
The basic digital building blocks for AND and OR can be combined with the NOT, inverter. The symbol used is a circle on the output.
NAND: Is a NOT-AND . Its output = 1, only if both inputs are not 1. ____ Boolean Expression: A • B
Logic Gate:
Truth Table:
The NAND functions has traditionally been the universal gate in digital circuits. It is simple to implement in hardware and can be used to construct the other gates.
A
B C
A B C
0 0 1
0 1 1
1 0 1
1 1 0
More Logic Gates
· NOR: Is a NOT-OR. Its output = 1 only if no input = 1.
_____ Boolean Expression: A + B
Logic Gate:
Truth Table:
A
B
C
A B C
0 0 1
0 1 0
1 0 0
1 1 0
More Logic Gates
· XOR: Is an EXCLUSIVE-OR. Its output = 1 if the inputs are different and equal 0 if all are the same .
Boolean Expression: A B
Logic Gate:
Truth Table:
_ _ Logical equivalent: (A•B) + (A•B) = C
A B C
0 0 0
0 1 1
1 0 1
1 1 0
AC
B
More Logic Gates
· XNOR: Is an EXCLUSIVE-OR. Its output = 1 if the inputs are different and equal 0 if all are the same .
Boolean Expression: A B
Logic Gate:
Truth Table:
_ _ Logical equivalent: AB + AB = C
A B C
0 0 1
0 1 0
1 0 0
1 1 1
AC
B