A binary truth table maps every possible combination of digital inputs (0 or 1) to a single deterministic output for a logic gate. However, for physical integrated circuits like the 7400 (TTL/CMOS) and 4000 (CMOS) series, those 1s and 0s are not abstract math. They are specific voltage thresholds dictated by the logic family you select. If you are debugging a breadboard or designing a custom PCB, reading the table correctly means translating Boolean algebra into real-world multimeter measurements.
The Standard Binary Truth Table for Basic Logic Gates
The following table defines the foundational logic operations based on the IEEE 315-1975 and IEC 60617 graphic symbol standards. Bookmark the specific rows you query most often using the anchor IDs provided.
| Input A | Input B | AND (74x08) | OR (74x32) | NAND (74x00) | NOR (74x02) | XOR (74x86) | XNOR (74x266) |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 |
| 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 |
| 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 |
| 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 |
Which Voltage Threshold Column Applies to Your Circuit
The binary truth table assumes ideal 1s and 0s. In practice, your multimeter will read analog voltages. Which voltage qualifies as a '1' depends entirely on the logic family column you are working with. Mixing these up is the number one cause of 'ghost' logic states on the bench.
- 74LS Series (TTL): Strictly a 5V system. A logic '0' ($V_{IL}$) is anything below 0.8V. A logic '1' ($V_{IH}$) requires a minimum of 2.0V. If your microcontroller outputs 3.3V, it will successfully drive a 74LS input high, but you are operating with a reduced noise margin.
- 74HC Series (High-Speed CMOS): Operates from 2.0V to 6.0V. The thresholds are proportional to your supply voltage ($V_{CC}$). A logic '1' requires at least 0.7 × $V_{CC}$. If you power a 74HC08 at 5V, you need 3.5V to guarantee a '1'. If you power it at 3.3V, you need 2.31V.
- 74HCT Series (TTL-Compatible CMOS): Runs at 5V but features TTL-compatible input thresholds ($V_{IH}$ = 2.0V). Use this when interfacing older 5V TTL outputs or 3.3V microcontrollers to a 5V logic bus.
- CD4000B Series (Standard CMOS): Operates from 3V to 15V. Like the HC series, thresholds are proportional to $V_{CC}$ (typically 0.7 × $V_{CC}$ for a '1'). Excellent for high-voltage battery applications, but too slow for high-speed digital buses.
How Active-Low Modifiers Invert the Base Output
In wire sizing, derating factors modify your base ampacity. In digital logic, active-low pins modify your base truth table. When you see a bar over a pin name (e.g., $\overline{RESET}$, $\overline{CS}$, or $\overline{EN}$) or a small circle (bubble) on an IEC 60617 logic symbol, the standard truth table is inverted for that specific control line.
If a multiplexer like the 74HC151 has an active-low Enable pin ($\overline{E}$), the binary truth table for the device's outputs is entirely overridden if $\overline{E}$ is HIGH (1). The chip ignores the data inputs and forces all outputs to a specific state (usually LOW or high-impedance). When debugging, always trace and verify active-low control pins first. A floating $\overline{RESET}$ pin picking up ambient EMI will randomly invert your expected truth table outputs, making the IC appear defective when it is actually just lacking a pull-up resistor.
Decision Path: Selecting the Right Logic IC Family
Use this decision tree to terminate your part selection with a concrete pick. Do not mix families on the same breadboard without checking voltage thresholds.
| Circuit Condition | Required Action | Concrete IC Pick |
|---|---|---|
| Powered by a 3.3V microcontroller (ESP32/RP2040) | Must accept 3.3V as a valid HIGH without 5V tolerance issues. | 74HC series (run at 3.3V) or 74LVC series. |
| Interfacing 3.3V MCU to a 5V sensor bus | Needs 5V output but must recognize 3.3V as a valid HIGH input. | 74HCT series (e.g., 74HCT245 buffer). |
| Running off a 9V or 12V battery supply | Needs wide voltage tolerance; speed is secondary. | CD4000B series (e.g., CD4011 NAND). |
| Handling noisy mechanical switch inputs | Standard gates will cause multiple triggers due to contact bounce. | 74HC14 (Hex Schmitt-Trigger Inverter). |
What the Binary Truth Table Cannot Tell You
A truth table is a static, idealized snapshot. It completely omits the dynamic, real-world physics that will break your circuit if ignored. Always cross-reference the Texas Instruments Logic Portfolio datasheets for these three missing variables:
- Propagation Delay ($t_{pd}$): When Input A transitions from 0 to 1, the output does not change instantaneously. A standard 74HC08 at 5V has a typical propagation delay of 14 nanoseconds. In a high-speed clock circuit, chaining five gates in series introduces a 70ns skew, which can cause race conditions and metastability in downstream flip-flops.
- Floating Inputs and Shoot-Through Current: The truth table assumes inputs are firmly tied to 0 or 1. If you leave a CMOS input (74HC or CD4000) unconnected, it acts as an antenna. The input voltage will drift into the linear region (between $V_{IL}$ and $V_{IH}$), causing both the internal PMOS and NMOS transistors to turn on simultaneously. This 'shoot-through' creates a direct short from $V_{CC}$ to GND, rapidly overheating and destroying the IC. Never leave a logic input floating; always use a 10kΩ pull-up or pull-down resistor.
- Fan-Out Limits: The table shows one output driving one theoretical load. In reality, a 74HC output can typically source or sink about 25mA. If you wire that single output to twenty 74LS inputs (which draw roughly 0.4mA each when LOW), you will exceed the 25mA sink limit, causing the output voltage to rise out of the valid logic '0' threshold. Calculate your total load current before branching a single gate output to multiple destinations.
