3-Input Logic Gate Truth Table & IC Selection Guide

A 3-input logic gate evaluates three binary inputs (A, B, and C) to produce a single binary output. Because there are three inputs, there are exactly eight possible input combinations ($2^3 = 8$). While the boolean math is straightforward, translating that truth table into a physical circuit requires selecting the right logic family, managing voltage thresholds, and accounting for propagation delay derating. Below is the complete reference data, followed by a concrete decision path to select your exact IC part number.

The Complete 3-Input Logic Gate Truth Tables

The following table defines the output states for the four standard 3-input gates: AND, NAND, OR, and NOR. The logic conventions and graphic symbols referenced here comply with ANSI/IEEE Std 91-1984 (Graphic Symbols for Logic Functions) and standard positive logic (where a higher voltage represents a logical '1').

Which Logic Column Applies to Your Installation?

The truth table above assumes positive logic (Active-High), which is the default for 95% of hobbyist and commercial digital designs. However, you must verify which voltage column applies to your specific physical installation based on your logic family:

• 5V CMOS (74HC series): A logical '1' requires a minimum input voltage ($V_{IH}$) of 3.15V. A logical '0' ($V_{IL}$) must be below 1.35V. Voltages between 1.35V and 3.15V are in the undefined region and will cause unpredictable output toggling.
• 5V TTL (74LS series): A logical '1' requires a minimum $V_{IH}$ of 2.0V. A logical '0' must be below 0.8V. Notice the wider undefined region compared to CMOS.
• 3.3V CMOS (74LVC series): $V_{IH}$ is typically 2.0V, and $V_{IL}$ is 0.8V. Crucial note: Many 74LVC gates are 5V-tolerant on their inputs, meaning you can safely feed them 5V TTL signals without a level shifter, but always check the specific datasheet.
• Negative Logic (Active-Low): If your schematic uses bubble notation on the inputs, the physical voltage column is inverted. A physical '0' (GND) is interpreted as a logical '1'. In this case, an active-low 3-input AND gate behaves electrically identically to a standard 3-input OR gate.

Propagation Delay and Fan-Out Derating

A truth table tells you what the output will be, but not when. In high-speed circuits, propagation delay ($t_{pd}$) and fan-out derating modify the base values provided in manufacturer datasheets.

Base propagation delay is typically measured at a standard capacitive load ($C_L$) of 50 pF. When you wire the output of your 3-input gate to multiple downstream inputs, you add parasitic capacitance. Here is how derating modifies the base value:

• The Rule of Thumb: For standard 74HC logic at 5V, add approximately 1.2 ns to 1.5 ns of propagation delay for every 15 pF of added load capacitance beyond the base 50 pF.
• Fan-Out Limits: A single 74HC output can typically drive 10 standard 74HC inputs (fan-out of 10). If you exceed this, the increased capacitive load will degrade the rise/fall times ($t_r/t_f$), potentially causing the signal to spend too much time in the undefined linear region, leading to thermal runaway and IC destruction.
• Voltage Derating: Running a 74HC chip at 3.3V instead of 5V roughly doubles the propagation delay. If your timing budget is tight, you must use the 3.3V derating curves from the datasheet, not the 5V typicals.

IC Selection Decision Path

Use this decision tree to terminate your search with a concrete, purchasable part number. Do not mix logic families on the same bus without checking $V_{IH}/V_{IL}$ compatibility.

Default Recommendation: If you are building a new 5V or 3.3V project on a breadboard and have no strict nanosecond-level timing constraints, buy the 74HC series (e.g., SN74HC11N for the DIP-14 through-hole package). It offers the best balance of low static power draw, wide voltage tolerance (2V to 6V), and high noise margins. For detailed electrical characteristics, refer to the Texas Instruments SN74HC11 Datasheet.

What the Truth Table Cannot Tell You

A truth table represents an idealized, static universe. It assumes inputs change instantaneously and perfectly synchronized. In physical reality, you must account for three phenomena that the table hides:

1. Floating Inputs and Oscillation

The truth table assumes inputs are firmly at '0' or '1'. In CMOS logic (74HC, CD4000), a floating (unconnected) input acts as a high-impedance antenna. It will pick up ambient electromagnetic noise, causing the gate's internal MOSFETs to rapidly switch on and off. This results in massive current draw (often exceeding the IC's absolute maximum ratings) and high-frequency oscillation on the output. Fix: Never leave an unused 3-input gate pin floating. Tie unused inputs to VCC or GND, or tie them to a used input.

2. Transient Glitches (Race Conditions)

Look at the transition from Row 4 (0,1,1) to Row 7 (1,1,0) in an OR gate. The output should remain '1'. However, if Input A goes high slightly after Input C goes low, the gate will briefly see the state (0,1,0) or (0,0,0) for a few nanoseconds. This causes a momentary '0' glitch on the output. Fix: If your downstream circuit is edge-triggered (like a clock input on a flip-flop), use a strobe signal or a Karnaugh-map optimized design with redundant logic terms to mask these hazards.

3. Metastability

If you are feeding the output of your 3-input gate into a sequential logic element (like a D-flip-flop) driven by a clock, the truth table won't warn you about setup and hold times. If the gate's output changes state within the critical window (typically a few nanoseconds) around the clock edge, the flip-flop can enter a metastable state, outputting an invalid voltage level or oscillating before resolving. Fix: Ensure your combinational logic path delay is strictly greater than the flip-flop's hold time requirement, and less than the clock period minus the setup time.