Multi-Input Gates

A 74HC30 8-input NAND sits inside every PC motherboard's chipset, performing bus grant logic in a single package. Multi-input gates shrink gate count drastically over cascaded 2-input designs.

Core Concept

A multi-input gate extends a basic 2-input operation to three or more inputs. The output logic is the same — AND requires all inputs HIGH, OR requires any input HIGH — but the number of input terminals grows. The 74HC10 triple 3-input NAND provides three independent 3-input NAND gates in a single 14-pin package.

Multi-input gates reduce propagation delay compared to cascading 2-input gates. A 3-input AND built from one 74HC11 has 7 ns delay. The same function built from two 74HC08 gates in cascade has 14 ns delay — double. For time-critical paths, single multi-input gates are always preferred.

The 74HC30 is an extreme case: a single 8-input NAND gate in a 14-pin DIP. It computes Y = (A·B·C·D·E·F·G·H)' in 8 ns at 5 V. Bus-grant and interrupt-priority circuits use it to detect when all eight conditions are met simultaneously.

Boolean Expression

For an N-input AND: Y = A₁ · A₂ · ... · Aₙ. For N-input NAND: Y = (A₁ · A₂ · ... · Aₙ)'. The truth table has 2ⁿ rows. For NAND the output is LOW only when all N inputs are HIGH — all other 2ⁿ−1 input combinations give HIGH output.

Given:
  3-input NAND gate (74HC10)
  Evaluate Y for inputs: A=1, B=1, C=0

Formula / Rule:
  Y = (A · B · C)'

Step by step:
  Step 1: Compute AND: A·B·C = 1·1·0 = 0
  Step 2: Invert:      Y = 0' = 1

Check another input (A=1, B=1, C=1):
  Step 1: A·B·C = 1·1·1 = 1
  Step 2: Y = 1' = 0   (NAND is LOW only when all inputs HIGH)

Check (A=0, B=0, C=0):
  Step 1: A·B·C = 0
  Step 2: Y = 0' = 1

Final Answer:
  Y=0 only when A=B=C=1
  Y=1 for all 7 other input combinations
  Truth table has 8 rows (2^3), only 1 row gives Y=0

Exam Tip: For an N-input NAND, the output is LOW for exactly ONE combination (all inputs HIGH). For an N-input NOR, the output is HIGH for exactly ONE combination (all inputs LOW). GATE problems often ask how many input combinations produce a specific output — compute 2^N and subtract. Also: the 74HC30 8-input NAND has only 2 unused pin positions in a 14-pin package — a common package-counting question.

Key Properties

• 74HC11 triple 3-input AND: 7 ns at 5 V, 2–6 V supply, fan-out 10
• 74HC10 triple 3-input NAND: 7 ns at 5 V, single-package solution
• 74HC30 8-input NAND: 8 ns at 5 V, one gate per package, 14-pin DIP
• 74HC27 triple 3-input NOR: 7.5 ns at 5 V, useful for active-low interrupt logic
• N-input NAND output LOW for exactly 1 of 2ⁿ input combinations
• N-input NOR output HIGH for exactly 1 of 2ⁿ input combinations
• Cascading 2-input gates doubles propagation delay versus a single multi-input gate

Quick Revision

• N-input AND: Y=1 only when all N inputs are 1
• N-input NAND: Y=0 only when all N inputs are 1 (1 row in truth table)
• N-input NOR: Y=1 only when all N inputs are 0 (1 row in truth table)
• 74HC10 triple 3-input NAND: 7 ns, 5 V, fan-out 10
• 74HC30 single 8-input NAND: 8 ns, 14-pin DIP
• Single multi-input gate is faster than cascaded 2-input gates by one gate delay
• Truth table rows = 2^N for N input variables
• Exam trap: assuming a 3-input NAND has only 1 input combination giving Y=1 — it is actually 7 out of 8, with only 1 giving Y=0