All Logic Gate Truth Tables: Reference Chart and IC Selection Guide

When you are debugging a digital circuit or designing a custom control board, you need two things: the theoretical boolean output for a given input state, and the physical integrated circuit (IC) that will actually execute that logic at your target voltage. The truth table gives you the first; the logic family specification gives you the second. Below is the definitive bench reference for all logic gate truth tables, mapped directly to the physical ICs you need to order.

The Master Logic Gate Truth Table Reference

The following table defines the standard 2-input and 1-input logic gates. The boolean expressions and output states are standardized under IEEE Std 91-1984 and IEC 60617-12. Use the quick-jump IDs to bookmark specific gates for fast lookup during bench testing.

How to Read the Table and Select Your Logic Family Column

A truth table only tells you the mathematical relationship between inputs and outputs. It does not tell you what voltage constitutes a logical "1" or "0". To determine which column applies to your installation, you must cross-reference your system's VCC (supply voltage) and operating temperature with the logic family specifications.

Propagation Delay and Capacitive Load Derating

The truth tables above assume an instantaneous transition from 0 to 1. In physical silicon, this is false. Every gate has a propagation delay ($t_{pd}$), and this base value is heavily modified by capacitive loading and fan-out. When you read a datasheet, the base $t_{pd}$ is typically measured at a specific load (e.g., $C_L = 50pF$). As you add more gates to the output (increasing fan-out) or route long PCB traces (increasing parasitic capacitance), the delay derates upward.

Worked Example: You are using a Texas Instruments SN74HC00 NAND gate at 5.0V. The datasheet lists a typical $t_{pd}$ of 8ns with a 50pF load. If your PCB trace and the inputs of the three downstream gates total 150pF of capacitance, the delay derates by roughly 0.1ns per picofarad of additional load. Your actual propagation delay will be closer to 18ns. If you are clocking this logic at 50MHz (20ns period), this derating will cause setup-time violations and erratic behavior. You must either reduce the trace length, buffer the output, or switch to a faster family like 74AHC.

Decision Tree: Picking the Exact IC Part Number

Use this decision path to terminate your selection process and order the correct physical component. Do not mix families on the same data bus without checking voltage thresholds.

What the Truth Table Cannot Tell You

Relying solely on boolean truth tables leads to three common hardware failures on the bench. The truth table is a mathematical abstraction; it completely ignores the physical realities of silicon.

1. Floating Inputs and Shoot-Through Current: The truth table does not show what happens when an input is left unconnected (floating). In CMOS families (74HC, CD4000), a floating input will drift into the linear region between the internal PMOS and NMOS transistors. Both transistors turn on simultaneously, creating a low-resistance path from VCC to GND. The IC will overheat, draw excessive current, and potentially destroy itself. Fix: Always tie unused CMOS inputs to VCC or GND via a 10kΩ resistor.
2. Metastability: If an input signal changes state at the exact nanosecond the clock edge triggers a flip-flop (which is built from these basic gates), the output may enter a metastable state—hovering between 0 and 1 or oscillating rapidly. The truth table has no row for "undefined." Fix: Use synchronizer flip-flops for asynchronous external signals.
3. Current Sourcing vs. Sinking Limits: The truth table says a logical "1" outputs HIGH. It does not tell you that a standard 74HC gate can only source about 4mA to 6mA per pin. If you try to drive a 20mA indicator LED directly from the output of a 74HC08 AND gate without a transistor buffer, the output voltage will sag below the valid logic HIGH threshold, and the IC will overheat. Fix: Use a 2N2222 BJT or a 2N7000 MOSFET to switch loads heavier than 4mA.

For 90% of modern DIY and prototyping applications, the 74HC family at 5.0V is the definitive default. It offers the best balance of propagation delay, power consumption, and compatibility with standard microcontrollers. Keep the All About Circuits digital logic reference bookmarked for deeper boolean simplification, but rely on the family columns and derating curves above when it is time to actually wire the breadboard.