Basic Logic Gates | Types of Logic Gates In Digital Electronics

This post covers the theoretical explanations and fundamental concepts behind basic digital logic gates: NOT (Inverter), Buffer (BUF), NAND, NOR, XOR, and XNOR. Each gate plays a critical role in electronic circuit design, making logical decisions based on binary signals and forming the building blocks of complex digital systems.

Core Concepts

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NOT Gate (Inverter)

A NOT gate has a single input and a single output. Its purpose is to invert the logical value it receives. If the input is high (logic 1), the output becomes low (logic 0), and if the input is low, the output flips to high.

• Mathematical representation: If input is $X$, then output is $X'$ or $\overline{X}$, which denotes the complement of $X$.
• Logical operation: $Y = \overline{X}$

Buffer Gate (BUF)

A Buffer gate simply passes its input unchanged to the output. It does not alter the signal, but can be used to strengthen (amplify) a signal, introduce a delay, or protect circuit components from direct interaction.

• Mathematical representation: For input $X$, output $Y = X$

NAND Gate

The NAND gate combines the actions of AND and NOT gates. It outputs a low signal only when all inputs are high; otherwise, the output is high. For two inputs, $X$ and $Y$, its output is the inverted result of the AND operation.

• Mathematical representation: $Y = \overline{X \cdot Y}$
• Key property: Universal gate—can synthesize any other logic function using only NAND gates.

NOR Gate

A NOR gate inverts the outcome of the OR gate. It only outputs high when all inputs are low; any high input turns the output low. For inputs $X$, $Y$, output is the inverted OR.

• Mathematical representation: $Y = \overline{X + Y}$

XOR Gate (Exclusive OR)

The XOR gate outputs high only when the inputs are different. If both inputs are the same, the output is low. It is used where logical distinction or comparison is needed.

• Mathematical representation: $Y = X \oplus Y$ (the $\oplus$ symbol denotes exclusive OR)
• Decision logic: Output is true if $X \neq Y$

XNOR Gate

The XNOR gate (Exclusive NOR) outputs high only when both inputs are equal, whether both are high or both are low. It is essentially the complement of XOR.

• Mathematical representation: $Y = \overline{X \oplus Y}$
• Application: Used to detect equality between two signals.

Key Points

• NOT gate inverts its single input: $Y = \overline{X}$
• Buffer gate transmits its single input unchanged: $Y = X$
• NAND gate outputs low only if all inputs are high: $Y = \overline{X \cdot Y}$
• NOR gate outputs high only if all inputs are low: $Y = \overline{X + Y}$
• XOR gate outputs high only when inputs are different: $Y = X \oplus Y$
• XNOR gate outputs high only when inputs are equal: $Y = \overline{X \oplus Y}$

• NAND and NOR are known as universal gates because any digital logic circuit can be constructed using only NAND or only NOR gates.
• Buffers enhance signal integrity and can provide isolation between circuit segments.
• XOR and XNOR gates are essential in arithmetic operations, error detection, and equality comparisons in digital systems.