Translating a theoretical boolean truth table into a physical circuit requires matching logical operations to specific integrated circuit (IC) part numbers. The direct answer for most modern 5V or 3.3V hobbyist and prototyping applications is the 74HC series (e.g., 74HC08 for AND, 74HC32 for OR). For higher voltage or legacy battery-powered systems, the CD4000B series is the standard. Below is the master reference chart mapping basic truth tables to physical silicon, followed by the engineering constraints that datasheets hide from beginners.
The Master Truth Table to Logic Gate Reference Chart
How to read this table: This chart maps the fundamental boolean operations to their most common physical IC implementations. The Logic Family / Voltage column dictates your physical installation environment (e.g., 3.3V microcontrollers vs. 12V automotive). The Base tpd (propagation delay) is measured under standard JEDEC testing conditions (typically 25°C, 15pF capacitive load, 5V VCC). Pinouts follow standard DIP-14 configurations unless noted. Symbol graphics conform to IEEE Std 91-1984 graphic symbols for logic functions.
| Gate Type | Boolean | 74HC Series (2V-6V) | CD4000B Series (3V-15V) | Base tpd (ns) | Max Fan-Out (LS-TTL) |
|---|---|---|---|---|---|
| AND (2-Input) | A · B | 74HC08 | CD4081 | 18 | 25 |
| OR (2-Input) | A + B | 74HC32 | CD4071 | 18 | 25 |
| NOT (Inverter) | A' | 74HC04 | CD4069 | 14 | 25 |
| NAND (2-Input) | (A · B)' | 74HC00 | CD4011 | 18 | 25 |
| NOR (2-Input) | (A + B)' | 74HC02 | CD4001 | 18 | 25 |
| XOR (2-Input) | A ⊕ B | 74HC86 | CD4070 | 22 | 25 |
| XNOR (2-Input) | (A ⊕ B)' | 74HC266 | CD4077 | 30 | 25 |
Applying the Chart: Voltage Families and Timing Derating
Which Voltage Family Column Applies to Your Installation
The choice between the 74HC and CD4000B columns depends entirely on your supply voltage and signal thresholds. If you are interfacing with a 3.3V ESP32 or Raspberry Pi, you must use the 74HC (or 74LVC) column. The CD4000B series requires higher voltage swings to reliably register a logic HIGH at 3.3V and is far too slow for high-speed SPI or I2C bus buffering. Conversely, if you are building a 12V automotive logic circuit or a 9V battery-powered synth module, the CD4000B column applies, as 74HC chips will violently fail if VCC exceeds 6V.
How Timing Derating Modifies Base Values
The Base tpd column in the table above is a best-case scenario. In physical installations, propagation delay derates based on two factors: capacitive load (CL) and ambient temperature. According to the Texas Instruments SN74HC08 Datasheet, the base 18ns delay assumes a 15pF load. If you wire the output to a long breadboard bus or daisy-chain it into 5 other gate inputs (increasing CL to ~50pF), the delay derates to approximately 28ns. Furthermore, operating at the upper limit of 85°C adds roughly 15% to the delay. If your truth table involves high-frequency clock division, you must calculate the derated delay to ensure your setup and hold times are not violated.
What This Table Cannot Tell You
A truth table assumes ideal, instantaneous state changes. The physical IC reference table cannot tell you about metastability or shoot-through current. If an input voltage hovers exactly at the VCC/2 threshold (e.g., a slowly rising analog ramp fed into a digital input), both the internal PMOS and NMOS transistors turn on simultaneously. This creates a dead-short from VCC to GND inside the silicon, causing the IC to overheat and the output to oscillate wildly. The table also omits the absolute requirement for power supply decoupling: every single logic IC on your board requires a 100nF (0.1µF) ceramic bypass capacitor placed within 2mm of its VCC and GND pins to prevent ground bounce from corrupting your truth table outputs.
Quick-Jump Rows for the Most Queried Combinations
For rapid prototyping, bookmark these specific part mappings for the most common bench scenarios:
- I need a simple inverter for a clean digital signal: Use the 74HC04 (Hex Inverter). You get six independent NOT gates in one DIP-14 package.
- I need an inverter for a noisy mechanical switch or slow analog ramp: Use the 74HC14 (Hex Schmitt-Trigger Inverter). The built-in hysteresis prevents the output from oscillating when the input crosses the threshold slowly.
- I need to combine three signals (A AND B AND C): Cascade two gates from a 74HC08 (e.g., Output of Gate 1 feeds Input A of Gate 2), or use a dedicated 3-input AND gate like the 74HC11.
- I need to build any arbitrary truth table using only one IC type: Stock up on 74HC00 (Quad 2-Input NAND). NAND gates are 'universal'; you can wire them to act as NOT, AND, OR, or any other gate.
Frequently Asked Questions (FAQ)
How do I convert a multi-input truth table to standard 2-input logic gates?
Standard 74HC and CD4000 series ICs primarily feature 2-input gates (with some 3-input and 8-input exceptions). To implement a 3-input truth table (e.g., Y = A · B · C), you cascade two 2-input gates. Feed A and B into the first 74HC08 AND gate. Take the output of that gate and feed it into the A input of a second AND gate on the same chip, with C connected to the B input. For complex Sum-of-Products (SOP) truth tables, use De Morgan's Laws to convert the boolean expression entirely into NAND or NOR logic, minimizing the total IC count.
What is the difference between 74HC, 74HCT, and 74LS when reading a truth table?
The truth table (the logic) is identical for all three, but the electrical physics differ drastically. 74LS (Low-power Schottky) is legacy 5V TTL technology; it draws high current and outputs a weak logic HIGH (~3.4V). 74HC is modern CMOS, featuring rail-to-rail outputs and very low static power draw, but its input thresholds scale with VCC. 74HCT uses CMOS internals but features fixed TTL-compatible input thresholds (VIH = 2.0V), making it the perfect bridge chip when a 5V Arduino (using 74LS-style outputs) needs to talk to modern 3.3V logic.
Can I use a NAND gate to build any other logic gate from my truth table?
Yes. NAND (and NOR) gates are mathematically 'universal'. If your truth table requires an inverter, tie both inputs of a 74HC00 NAND gate together. To make an AND gate, pass the NAND output through a second NAND gate configured as an inverter. To make an OR gate, invert both inputs before feeding them into the NAND gate. While this works perfectly in theory and on a breadboard, be aware that cascading multiple NAND gates to simulate an OR gate adds cumulative propagation delay (tpd), which can cause timing glitches in high-speed clock circuits.
Why does my physical logic gate output not match the theoretical truth table?
If your multimeter or logic analyzer shows erratic outputs that defy the truth table, the culprit is almost always floating inputs. CMOS inputs (like the 74HC series) have incredibly high impedance. If an input pin is left unconnected, it acts as an antenna, picking up 50/60Hz mains hum and electromagnetic interference. This causes the internal transistors to switch rapidly, resulting in a metastable output and excessive chip heating. Always tie unused inputs to either VCC or GND using a 10kΩ resistor, and ensure your mechanical switches use pull-down or pull-up resistors to guarantee a solid logic LOW or HIGH.
