Introduction to Logic Gates

Part 1: What are Logic Gates?

Logic gates are the fundamental building blocks of digital circuits. They perform logical operations on one or more input bits and produce a single output bit. These operations are based on Boolean algebra, a mathematical system for representing and manipulating logical expressions. Common types of logic gates include AND, OR, NOT, NAND, NOR, XOR, and XNOR gates. Each gate has a unique symbol and truth table that defines its behavior. Logic gates are used in a wide range of applications, from computers and digital electronics to communication systems.

Part 2: Types of Logic Gates

When interpreting the basic logic gates, we can relate it to a basic circuit that have power source or power supply, switches as an input, bulb as an output.

Part 2.1: AND Gate

An AND gate is a digital logic gate that produces a high output (1) only when all of its inputs are high (1). If any of the inputs are low (0), the output will be low (0). In simpler terms, an AND gate acts like a logical "and" statement. It requires all conditions to be true (inputs to be 1) for the result (output) to be true (1).

Related Circuit:

A light bulb connected to two switches will only turn on when both switches are in the on position. This is similar to an AND gate, where both inputs must be 1 for the output to be 1.

Symbol:

Boolean Expression:

x ‧ y = F

Truth Table:

Input		Output
x	y	F
0	0	0
0	1	0
1	0	0
1	1	1

Part 2.2: OR Gate

An OR gate is a digital logic gate that produces a high output (1) when at least one of its inputs is high (1). If all inputs are low (0), the output will be low (0). In simpler terms, an OR gate acts like a logical "or" statement. It requires at least one condition to be true (input to be 1) for the result (output) to be true (1).

Related Circuit:

A light bulb with two switches will turn on as long as at least one of the switches is in the on position. This is similar to an OR gate, where one or both inputs must be 1 for the output to be 1.

Symbol:

Boolean Expression:

x + y = F

Truth Table:

Input		Output
x	y	F
0	0	0
0	1	1
1	0	1
1	1	1

Part 2.3: NOT Gate

Symbol:

Boolean Expression:

x = F’ or x =

Truth Table:

Input	Output
x	F
0	1
1	0

Part 2.4: NOR Gate

A NOR gate is a digital logic gate that produces a high output (1) only when all of its inputs are low (0). If any of the inputs are high (1), the output will be low (0).

In simpler terms, a NOR gate is the combination of an OR gate and a NOT gate. It first performs the OR operation on the inputs, then inverts (negates) the result.

Symbol:

Boolean Expression:

Truth Table:

Input		Output
x	y	F
0	0	1
0	1	0
1	0	0
1	1	0

Part 2.4: NAND Gate

A NAND gate is a digital logic gate that produces a low output (0) only when all of its inputs are high (1). If any of the inputs are low (0), the output will be high (1).

In simpler terms, a NAND gate is the combination of an AND gate and a NOT gate. It first performs the AND operation on the inputs, then inverts (negates) the result.

Symbol:

Boolean Expression:

Truth Table:

Input		Output
x	y	F
0	0	1
0	1	1
1	0	1
1	1	0

Part 2.4: Exclusive OR or XOR Gate

An XOR (eXclusive OR) gate is a digital logic gate that produces a high output (1) only when the inputs are different. If both inputs are the same (either both 0 or both 1), the output will be low (0).

In simpler terms, an XOR gate acts like a logical "exclusive or" statement. It requires only one of the conditions to be true (input to be 1) for the result (output) to be true (1), but not both.

Symbol:

Boolean Expression:

Truth Table:

Input		Output
x	y	F
0	0	0
0	1	1
1	0	1
1	1	0

Part 2.4.1: Equivalent Circuit of XOR Gate

An XOR gate can be constructed using a combination of AND, OR, and NOT gates. One common method involves using two AND gates to create product terms for each input being different, followed by an OR gate to combine these terms. Another approach utilizes NAND gates to create the complements of the AND and inverted inputs, then combines them using an AND gate. Both methods effectively replicate the functionality of an XOR gate, producing a high output only when the inputs are different.

Part 2.5: Exclusive-Not OR or XNOR Gate

An XNOR (eXclusive NOR) gate is a digital logic gate that produces a high output (1) only when both inputs are the same. If the inputs are different, the output will be low (0).

In simpler terms, an XNOR gate is the combination of an XOR gate and a NOT gate. It first performs the XOR operation on the inputs, then inverts (negates) the result.

Symbol:

Boolean Expression:

Truth Table:

Input		Output
x	y	F
0	0	1
0	1	0
1	0	0
1	1	1

Part 2.5.1: Equivalent Circuit of XOR Gate

An XNOR gate can be implemented using a combination of AND, OR, and NOT gates. A common approach involves creating two product terms using AND gates: one for both inputs being the same and the other for both inputs being different. These product terms are then combined using an OR gate. This circuit effectively replicates the functionality of an XNOR gate, producing a high output only when both inputs are the same.