18-05-2012, 04:44 PM
Logic functions
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The NAND Gate
This is a NAND gate. It is a combination of an AND gate followed by an inverter. Its truth table shows this…
NAND gates have several interesting properties…
NAND(a,a)=(aa)’ = a’ = NOT(a)
NAND’(a,b)=(ab)’’ = ab = AND(a,b)
NAND(a’,b’)=(a’b’)’ = a+b = OR(a,b)
These three properties show that a NAND gate with both of its inputs driven by the same signal is equivalent to a NOT gate
A NAND gate whose output is complemented is equivalent to an AND gate, and a NAND gate with complemented inputs acts as an OR gate.
Therefore, we can use a NAND gate to implement all three of the elementary operators (AND,OR,NOT).
Therefore, ANY switching function can be constructed using only NAND gates. Such a gate is said to be primitive or functionally complete.
The NOR Gate
This is a NOR gate. It is a combination of an OR gate followed by an inverter. It’s truth table shows this…
NOR gates also have several
interesting properties…
NOR(a,a)=(a+a)’ = a’ = NOT(a)
NOR’(a,b)=(a+b)’’ = a+b = OR(a,b)
NOR(a’,b’)=(a’+b’)’ = ab = AND(a,b)
The XNOR Gate
This is a XNOR gate.
This functions as an
exclusive-NOR gate, or
simply the complement of
the XOR gate.
The switching algebra symbol
for this operation is , i.e.
1 1 = 1 and 1 0 = 0.