Logic Gate Truth Tables: IC Families, Timing, and Real-World Thresholds

A logic gate truth table defines the Boolean relationship between digital inputs and outputs. In theory, an AND gate outputs a 1 only when both inputs are 1. But on the workbench, a physical IC like the Texas Instruments SN74HC08 isn't just an abstract mathematical concept; it is a silicon device bound by voltage thresholds, propagation delays, and temperature derating. If you are designing a mixed-voltage system in 2026—say, interfacing a 3.3V ESP32 with a 5V relay board—relying solely on an idealized truth table will lead to floating inputs, metastability, and fried GPIO pins.

This reference guide provides the standard ANSI/IEEE truth tables, followed by the critical silicon specifications and derating charts that dictate how those logic gates actually behave in physical circuits.

The Master Logic Gate Truth Tables (ANSI/IEEE Std 91)

The following table covers the seven fundamental logic gates. The symbols and standard names align with ANSI/IEEE Std 91-1984, the standard for graphic symbols for logic functions.

Silicon Realities: Voltage Thresholds and Derating

An ideal truth table assumes that a '0' is exactly 0.0V and a '1' is exactly $V_{CC}$. Real silicon uses threshold windows: $V_{IL}$ (maximum voltage guaranteed to be read as a '0') and $V_{IH}$ (minimum voltage guaranteed to be read as a '1'). Furthermore, the transition between states takes time, known as propagation delay ($t_{pd}$).

When designing a circuit, which column applies to your installation depends entirely on your microcontroller's logic level and the ambient operating environment. If you are wiring a 3.3V Raspberry Pi Pico to a 5V sensor, you must look at the 74LVC or 74HCT columns, not the standard 74HC column.

How Derating Rows Modify the Base Value: Notice the $t_{pd}$ (Propagation Delay) columns. The 25°C row provides your base timing value for breadboard prototyping. However, the 85°C derating row modifies this base value to reflect silicon behavior under thermal load. For a 74HC gate, the delay increases from 12ns to 16ns. If you are chaining multiple gates in a high-speed clock divider or a ripple-carry adder, this 4ns derating penalty per gate accumulates. If your design relies on a 50MHz clock (20ns period), a single 74HC gate at 85°C consumes 80% of your timing budget, risking metastability.

What the Ideal Truth Table Cannot Tell You

While the truth table gives you the static logical outcome, it completely omits the dynamic and physical behaviors of the IC. When debugging a circuit on an oscilloscope, keep these three blind spots in mind:

1. Metastability and Setup/Hold Times: If inputs A and B of an XOR gate transition at the exact same nanosecond, the output doesn't just cleanly snap to '0'. It may enter a metastable state, oscillating or hovering at $V_{CC}/2$ for several nanoseconds before resolving. Truth tables assume inputs are stable; real silicon requires setup and hold time margins.
2. Floating Inputs (The CMOS Hazard): The truth table doesn't show what happens when an input is left unconnected. In bipolar TTL (74LS), a floating input defaults to a logical '1' due to internal pull-up structures. In CMOS (74HC, 74LVC), a floating input acts as an antenna. It will pick up EMI, causing the internal MOSFETs to rapidly switch on and off. This doesn't just cause erratic outputs; it causes massive $I_{CC}$ current spikes that can overheat and destroy the IC. Always tie unused CMOS inputs to GND or $V_{CC}$.
3. Output Drive Capability (Fan-Out): A truth table shows a '1', but it doesn't tell you how much current that '1' can source. A standard 74HC gate can typically source/sink about 25mA. If your truth table says '1', but you've connected an LED without a current-limiting resistor, the output voltage will droop below the $V_{IH}$ threshold of the next gate, or the silicon trace will fuse open.

Quick-Jump Reference: Common 74-Series IC Part Numbers

When you need to order parts or swap a dead chip on a legacy PCB, use this bookmark-friendly lookup. These part numbers assume the standard 14-pin PDIP or SOIC packages containing quad 2-input gates (or hex inverters).