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# Truth Tables for Digital Logic

Truth tables list-out the output of a particular digital logic circuit for all the possible combinations of its inputs. This means that these truth tables can be used to deduce the logical expression for the given digital circuit.

### NOT Gate or an Inverter

NOT gate is a single-in single-out logical device where the output will always be the complementary form of the input. This means that the output is 0 for input equal to 1 and vice versa, as indicated by the truth table. This is symbolically written as Y = X̅.

### AND Gate

AND gate is a basic gate with multiple inputs and a single output. This gate has its output high only if all its inputs are one, failing which the output will be zero as shown by the truth table. The logical expression corresponding to this gate is given as Y = I1.I2.

### OR Gate

OR is a type of basic gate with multi-input, single-output characteristic. Here the output is zero only if all of its input bits are zero as indicated by the truth table of 2-input OR gate. The logical expression for the OR gate is given as

### NAND Gate

NAND gate is logically equivalent to AND gate followed by a NOT gate. The truth table for this gate shows that the output of NAND gate is low only if all of its inputs are high (else it is one). This implies that the output of the NAND gate is the negated output of the AND gate, represented by the intermediate result M in the above truth table. Logical expression for the NAND gate is given by

### NOR Gate

NOR gate is a result of combining NOT gate with an OR gate. Thus its output is the negation of OR gate output which implies that it has high output only if all of its inputs are low. However for any other combination of inputs, the output will be low as shown by the truth table. Logical expression for the same can be given as

### XOR Gate

XOR gate is a logical device which has its output high only when its inputs are different, as shown by the truth table. This means that non-identical inputs result in high output of the gate while identical input bits cause the gate output to go low.

Logically this is given by Further in its expanded form, one gets In general XOR gate is used as a parity checker and can have multiple inputs.

### XNOR gate

XNOR gate is a result of combining XOR gate with a NOT gate, which means that the output will be the inverted form of the XOR outputs. Thus one gets high output for identical inputs and low output for non-identical inputs, as shown by the truth table. Logical expression for the XNOR gate is given by This gate can also have multiple inputs and serves as a parity checker.

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