Overview: Logic Gates

• Discrete circuits use separate components connected by wires; they are bulky and less reliable.
• An integrated circuit (IC) is a complete circuit fabricated on a single silicon chip, making it compact and reliable.
• Monolithic ICs are the most common and integrate all components on a single silicon crystal.
• ICs are classified as analog (linear operation) and digital (discrete/binary operation).
• Based on the degree of integration, ICs are classified as SSI, MSI, LSI, VLSI, and ULSI, depending on the number of logic gates on a chip.

A signal having only two levels of voltage (or current) is called a 'digital signal'.

• Analogue signals vary continuously and can take any value in a range.
• Digital signals have only two levels: 0 and 1 (low and high voltage).
• Real-world quantities are mostly analogue, but computers use digital signals.
• Digital circuits work using ON and OFF states.
• Digital systems are accurate, reliable and free from noise

Logic gates are digital circuits which work according to some logical relationship between input and output signals.

OR

Logic _gates are the basic building blocks of a logic circuit. Logic circuit is a digital Circuit, a switching circuit that duplicates mental processes. The output of a logic circuit can be predicted from the conditions at the input terminals and hence there is a logical relationship between the input and output. So they are called logic gates.

The truth table of a logic gate is a table that shows all possible input combinations and the corresponding outputs for the logic gate.

OR

There are three basic logic gates: OR, AND and NOT. Their operation can be represented in a table, called the truth table.

The expression showing the combination of two Boolean variables that results into a new Boolean variable is known as 'Boolean expression'.

• An AND gate has two or more inputs and one output.
• The output is HIGH (1) only when all inputs are HIGH.
• The Boolean expression of the AND gate is
  Y = A · B
• The truth table shows that the output is 1 only for A = 1 and B = 1; otherwise, the output is 0.
• The AND gate can be realised using two switches in series or two diodes in a suitable circuit.

• Complex logic gates are formed by combining basic gates: AND, OR, and NOT.
• NAND gate = AND gate followed by NOT gate.
  Boolean expression: Y = (A · B)̅
  Output is 0 only when both inputs are 1.
• NOR gate = OR gate followed by NOT gate.
  Boolean expression: Y = (A + B)̅
  Output is 1 only when both inputs are 0.
• NAND and NOR are universal gates because they can perform all basic logic operations (AND, OR, NOT).
• A combination of gates is the basis of digital circuits used in calculators, computers, and electronic systems.

• NAND gate = AND gate followed by NOT gate.
  Boolean expression: Y = (A · \[\vec B\]).
• NAND is a universal gate because repeated use of NAND alone can produce AND, OR, and NOT gates.
• NOT gate from NAND:
  If both inputs are joined (A = B), then
  Y = (A · \[\vec A\]) = \[\vec A\], so NAND acts as a NOT gate.
• AND gate from NAND:
  Connect the output of a NAND gate to a NOT gate (made using NAND).
  Double negation gives Y = A · B.
• OR gate from NAND:
  First invert both inputs using NAND (to get \[\vec A\] and \[\vec B\]), then feed them into a NAND gate.
  Final output becomes Y = A + B (by De Morgan’s theorem).