Logic Gates: AND Gate Basics

Logic Gates

• A logic gate is a digital circuit that makes a decision based on one or more inputs.
• There are five types of logic gates: AND, OR, NOT, NAND, and NOR.

AND Gate

• The AND gate has 2 or more inputs and a single output.
• The output is HIGH (1) only when all inputs are HIGH (1).
• The Boolean expression for a 2-input AND gate is Y = A.B or Y = AB.
• The Boolean algebra for a 2-input AND gate is:
  • 0.0 = 0
  • 1.0 = 0
  • 0.1 = 0
  • 1.1 = 1
• The AND gate output is equal to the product of the logic inputs.

OR Gate

• The OR gate has 2 or more inputs and a single output.
• The output is HIGH (1) when any of the inputs are HIGH (1).
• The Boolean expression for a 2-input OR gate is Y = A + B.
• The Boolean algebra for a 2-input OR gate is:
  • 0+0 = 0
  • 1+0 = 1
  • 0+1 = 1
  • 1+1 = 1

NOT Gate

• The NOT gate is also known as an inverter.
• It has only one input and one output.
• The NOT gate inverts the input logic level.
• The Boolean expression for the NOT gate is Ā (read as A bar).
• Even number of NOT gates connected together, the output is equal to the input.
• Odd number of NOT gates connected together, the output is equal to the complement of the input.

NAND Gate

• The NAND gate is equivalent to an AND gate followed by an inverter.
• The NAND gate output is HIGH (1) when any of the inputs are LOW (0).
• The Boolean expression for the NAND gate is Y = Ā.B̄.

NOR Gate

• The NOR gate is equivalent to an OR gate followed by an inverter.
• The NOR gate output is HIGH (1) when both inputs are LOW (0).
• The Boolean expression for the NOR gate is Y = Ā + B̄.

Logic Circuit Output

• Once we have the Boolean expression for a circuit, we can determine the output logic level for any set of input levels.
• We can implement a logic circuit from a Boolean expression.