Basic Logic Gates

Logic gates are very important and they serve as the building blocks to digital logic circuits using combinational logic. We're going to consider the following gates: NOT gates (also called inverters), YES gates (also called buffer), AND gates, OR gates, NAND gates, NOR gates, XOR gates, and XNOR gates.

NOT gates or inverters have a single bit input and a single bit of output. This is a diagram of a NOT gate. It is a triangle with a circle on the right. The circle indicates:negation. YES gate symbol is without the circle indicates negation y its true table results are opposited to NOT gate.

AND gates have two bits of input and a single bit of output. The output of AND gate is 1 only if both inputs are 1. Otherwise, the output is 0. The function implmented by AND gates has interesting properties:

The function is symmetric. Thus, x * y == y * x. This can be verified by using truth tables. We use * to represent AND. The function is associative. Thus, (x * y) * z == x * (y * z). This can be verified by using truth tables.

OR gates have two bits of input and a single bit of output. The output of OR gate is 0 only if both inputs are 0. Otherwise, the output is 1. The function implemented by OR gates has interesting properties:

The function is symmetric. Thus, x + y == y + x. This can be verified by using truth tables. We use "+" to represent OR. The function is associative. Thus, (x + y) + z == x + (y + z). This can be verified by using truth tables.

NAND gates have two bits of input and a single bit of output. The output of NAND gate is the negation of AND. The function implemented by NAND gates have interesting properties: The function is symmetric. Thus, x NAND y == y NAND x. This can be verified by using truth tables.

OR gates have two bits of input and a single bit of output. The output of NOR gate is the negation of OR. The function implmented by NOR gates has interesting properties: The function is symmetric. Thus, x NOR y == y NOR x. This can be verified by using truth tables. The function is not associative. This can be verified by using truth tables.

XOR gates have two bits of input and a single bit of output. The output of XOR gate is 1 only if the inputs have opposite values. That is, when one input has value 0, and the other has value 1.. Otherwise, the output is 0. This is called exclusive-or. The function implmented by XOR gates has interesting properties: The function is symmetric. Thus, x (+) y == y (+) x. This can be verified by using truth tables.

XNOR gates have two bits of input and a single bit of output. The output of XNOR gate is the negation of XOR and has 1 when both inputs are the same. The function implmented by XNOR gates has interesting properties: The function is symmetric. Thus, x XNOR y == y XNOR x. This can be verified by using truth tables.