Digital Logic Basics

Chapter 7 dealt with signals that can take any voltage. This chapter is about the opposite: signals that are deliberately only ever one of two things, LOW or HIGH, 0 or 1. Everything inside a microcontroller works this way, and so do the small logic chips that sit around it on a robot: chips that combine switch signals, remember a button press, count wheel pulses, turn three pins into sixteen, or time a pulse with no program at all. A digital signal is tough: noise smaller than the gap between the two levels vanishes without trace, which is why a computer can copy a file perfectly while a tape cannot. The chapter uses the divider and pull-up ideas of Basic Electronics 3, the RC timing of Basic Electronics 4, the transistor switch of Basic Electronics 6 and the comparator with hysteresis of Basic Electronics 7. The mathematics of logic (Boolean algebra, simplification, adders) is a separate course, Boolean Algebra & Digital Logic; here we look at the electrical side: voltages, currents, chips and wiring.

1. Logic levels and noise margins

A digital input does not compare against exactly 2.5 V. Each chip family guarantees that a voltage below V_IL is read as LOW, a voltage above V_IH is read as HIGH, and that anything in between is undefined (it may read either, or oscillate). A driving output guarantees the opposite promise: its LOW is at most V_OL and its HIGH is at least V_OH, when supplying the rated current. For two chips to talk, the output's promise must fit inside the input's requirement; the room left over is the noise margin.

These figures are typical datasheet values at light load (74HC outputs quoted at 20 µA; at 4 mA, V_OL rises to about 0.26 V and V_OH falls to about 3.8 V). The datasheet of the exact part is the authority; the method is what matters.

Checking a connection: the two inequalities

2. Gates and truth tables

A gate is the smallest logic circuit: one output that is a fixed function of one or two inputs. The function is written as a truth table, which lists the output for every input combination (Boolean Algebra & Digital Logic 2 covers the operators and truth tables in depth; Boolean Algebra & Digital Logic 6 covers gates and how to combine them). The six you need every day:

Bubbles, bars and active-low names

A small circle on a gate symbol means inversion; a bar over a signal name (or a trailing # or _N or n) means active low: the signal does its job when it is LOW. A chip's CS̄ (chip select), RESET̄ and OĒ (output enable) are almost always active low, because open-drain wiring (section 5) and old TTL both pull more strongly low than high. When reading a datasheet, the name tells you which level means “yes”.

Why NAND is called universal

Any logic function can be built from AND, OR and NOT. A NAND gate can make all three, so a pile of NAND gates (a single 74HC00 holds four) can build any logic circuit; NOR has the same property. This is why chips and old computers were designed around one gate type.

3. Gates from transistors

A gate is only a few switches. Chapter 6 showed that a transistor is a switch that a voltage on its input can turn on or off; a logic gate is transistors arranged so that the output is pulled to LOW or HIGH by the right input combination.

Discrete NPN gates

The first logic circuits used bipolar transistors and resistors. With one NPN transistor and a pull-up resistor you have a NOT gate (input HIGH: transistor on, output pulled LOW; input LOW: transistor off, the resistor pulls the output HIGH). Put two transistors in parallel and the output goes LOW if either is on: a NOR. Put them in series and the output goes LOW only if both are on: a NAND. Build 1 builds the NAND.

Why this was replaced: the resistor conducts the whole time the output is LOW. With Rc = 1 kΩ on 5 V, that is (5 − 0.2)/1 kΩ = 4.8 mA per gate while LOW, so 100 gates draw half an ampere. A discrete gate also has a weak HIGH (it relies on a resistor that is slow when it must charge a wire's capacitance) and a switching threshold of about 0.7 V (one base-emitter drop), so noise margins are poor.

CMOS: complementary MOSFETs

Modern logic (the 74HC family and everything inside a microcontroller) uses pairs of MOSFETs, one P-channel device that conducts when its gate is LOW and one N-channel that conducts when its gate is HIGH. Wired complementary, one is always off:

4. Using the 74HC series

The 74HC chips are the standard small logic parts for hobby work: cheap, widely available in DIP (breadboard) packages, and with a supply range of 2 V to 6 V, so one chip serves a 5 V Arduino and a 3.3 V Pico. The 74HC chips are numbered by function (74HC00 is four NAND gates whichever maker sells it). Pinouts follow a pattern: the supply on the top corner, ground on the bottom corner, gate inputs and outputs in order. Read the datasheet before wiring a chip you have not used (the 74HC02 NOR chip, for example, puts the output first on each gate).

The rules that keep a 74HC chip working

• Never leave an input floating. A CMOS input has almost no leakage, so an unconnected pin floats to a random voltage picked up from the air (50 Hz hum, your hand), sits near the switching threshold where both transistors conduct (the chip then draws extra supply current and may get warm), and the output chatters. Tie every unused input to GND or VCC, and tie unused gates' inputs too (an unused gate is a gate with an unconnected input). Leave unused outputs unconnected.
• Decouple every chip: 100 nF ceramic across VCC and GND, as close to the chip's pins as the breadboard allows (Basic Electronics 4). When all the output transistors switch together, they pull a brief spike of current. Without the capacitor the spike drops the supply voltage by tens of millivolts or more, and other chips glitch.
• Respect the supply range. 74HC chips run from 2 to 6 V and are damaged above about 7 V. 74HCT is 4.5 to 5.5 V only. A 74HC chip powered from 3.3 V will not understand a 5 V input and may be destroyed by it (section 10).
• Never tie two normal outputs together. If one drives HIGH and another LOW the two outputs fight: the current is about 5 V / (60 Ω + 60 Ω) = 40 mA, which exceeds the rating and can destroy both. Where several devices must share one wire, use open-drain outputs (section 5) or a tri-state bus.
• Keep input edges fast. A plain 74HC input needs the voltage to cross the threshold quickly (the datasheet specifies a rise time of 500 ns or less at 4.5 V). A slow edge, such as the output of an RC network or a human-speed switch, lingers in the undefined region and gives multiple output pulses; this is the job of the Schmitt-trigger chips in section 6.

Fan-out and propagation delay

Typical figures; the datasheet of each part decides.

5. Pull-ups, pull-downs and open-drain outputs

Floating inputs and the switch

Basic Electronics 3 introduced the pull-up and pull-down resistor. It exists because a switch connects an input to only one of the two levels. With a button between the input and ground and nothing else, the input floats when the button is released. A 10 kΩ pull-up resistor to VCC supplies the other level:

Open-drain and open-collector outputs

A normal (totem-pole or push-pull) output has two switches: it drives HIGH and LOW. An open-drain output (MOSFET, as in 74HC03 or an I2C pin) or open-collector output (bipolar, as in an LM393 comparator, from Basic Electronics 7) has only the lower switch: it can pull the wire to ground or let go, and a pull-up resistor to a supply does the HIGH. Because the output cannot actively drive HIGH, many open-drain outputs can safely share one wire:

6. Schmitt-trigger inputs and debouncing

Basic Electronics 7 added hysteresis to a comparator with a resistor from output to input. A Schmitt-trigger input builds the same idea into a logic gate: the input has two thresholds, V_T+ for a rising signal and V_T− for a falling one. Once the output has switched, the input must travel the whole gap back before it switches again, so a slow or noisy edge produces one clean transition. The 74HC14 is a hex inverter with Schmitt inputs; 74HC132 is the NAND version.

Debouncing

A mechanical switch does not close cleanly. The contacts bounce, making and breaking for 1 to 10 ms (sometimes 20 ms) and producing a burst of pulses that a fast chip counts as many presses. Three cures:

1. Software: ignore further changes for about 20 ms after the first one. Free, and usual with a microcontroller.
2. RC filter plus a Schmitt gate (Basic Electronics 4 used the RC; here is the gate that makes it work):

3. A latch with a two-way (changeover, SPDT) switch: the first contact closing sets the latch, and bounce on the same contact changes nothing. See the SR latch in section 7. This is how the earliest hardware did it, and it needs no timing at all.

7. Latches and flip-flops: one bit of memory

All the circuits so far are combinational: the output depends only on the inputs now. A sequential circuit remembers: its output depends on what happened before. The smallest memory is two gates that feed each other (Boolean Algebra & Digital Logic 8 builds flip-flops and memory in logic terms).

The SR latch

With a changeover switch joined to ground, one throw to S̄ and the other to R̄ (each with its pull-up), the latch is a perfect debouncer: the first touch of a contact flips it and the later bounce changes nothing, because the other contact is already open and the first can only re-assert what it has set.

The D flip-flop and the 74HC74

A latch changes whenever its inputs do. A flip-flop samples its input only at an instant: the rising edge of a clock input. The D flip-flop is the commonest: on each rising clock edge, Q takes the value that D has at that moment, and keeps it until the next edge. Because the output changes at one instant, everything driven by the same clock changes together, and the glitches of section 4 are filtered out.

Toggle: divide a frequency by two

8. Counters and shift registers: more outputs and inputs from few pins

The counter: 74HC161

A counter is a row of flip-flops that counts clock pulses in binary. The 74HC161 is a 4-bit synchronous counter (all four flip-flops share the clock, so the outputs change together and do not glitch through wrong codes); the cheaper ripple counters like the 74HC4040 clock each stage from the previous one, so the outputs briefly show wrong codes while the edge ripples through (about 10 to 15 ns per stage).

The shift register: more outputs (74HC595)

A microcontroller never has quite enough pins. A serial-in, parallel-out shift register turns three output pins into eight (or sixteen, or sixty-four, by chaining): bits are pushed in one at a time on a data line, and then all eight leave together on the outputs.

The shift register in reverse: more inputs (74HC165)

9. The 555 timer

The 555 (1971 and still made) is the best-selling timing chip: two comparators, a flip-flop and a transistor in one 8-pin package, with a few resistors and a capacitor outside it. It makes a steady stream of pulses (the astable mode: a blinker, a clock, a PWM source) or one pulse of a set length when triggered (the monostable mode: a delay or a pulse stretcher). The ideas are all in this book already: a comparator (Basic Electronics 7), an RC charge curve (Basic Electronics 4) and an SR flip-flop (section 7).

Astable operation

Monostable operation

Which 555?

The builds use a TLC555 (the same pins as the NE555).

10. Level shifting between 3.3 V and 5 V

The parts of a robot do not all use the same voltage: an Arduino Uno or Nano is 5 V, but a Raspberry Pi Pico, an ESP32 and a Raspberry Pi are 3.3 V; many sensors, motor drivers and LED strips are 5 V. Joining a 3.3 V pin to a 5 V pin needs thought in both directions:

Down-shifting: a resistor divider

Up-shifting and the one-chip approach

For a 3.3 V board driving a 5 V device (a motor driver, an LED strip), use a 74HCT or 74AHCT buffer powered at 5 V: its input threshold is 2.0 V, so 3.3 V is a clean HIGH, and its output is a full 5 V. The 74AHCT125 (four buffers, with output-enable pins) is the usual chip; a 74HCT04 works too. Remember the NMH of 0.64 V: keep the wire short. For the other direction in a single chip, a 74LVC245 (eight-bit) or 74LVC125 powered at 3.3 V reads 5 V inputs safely and outputs 3.3 V. Ready-made modules with eight channels use these chips.

Both directions at once: the MOSFET shifter

An I2C bus is open-drain and works in both directions on the same wire, so it needs a bidirectional shifter. One N-channel MOSFET (BSS138 or 2N7000) per line does it:

11. Which board for logic work?

Basic Electronics 10 uses these chips from code and Basic Electronics 11 compares the boards in full.

12. Build it: a transistor NAND, a 555 blinker with a flip-flop, and a PWM motor-speed controller

Three small builds. Build 1 is a NAND gate made from two transistors, measured against a real 74HC00. Build 2 is a 555 blinker clocking a 74HC74 as a divide-by-two. Build 3 is the 555 as a pulse-width-modulation (PWM) speed control for a small DC motor, switched by the logic-level MOSFET of Basic Electronics 6.

Parts list

Build 1: a NAND gate from two transistors

Two NPN transistors in series with a collector resistor, as in section 3. The inputs are two jumper wires that you plug into the + rail (1) or the − rail (0).

1. Set A = 0, B = 0 (both jumpers on the − rail): OUT reads 5.0 V. Then A = 0, B = 1 and A = 1, B = 0: OUT still 5.0 V.
2. Set A = 1, B = 1: OUT drops to about 0.2 V; the voltage across R_c is about 4.8 V (4.8 mA); Q1's base reads about 0.8 V and Q2's about 0.7 V.
3. Leave input A unconnected (floating) with B = 1: OUT wanders: a floating input is neither HIGH nor LOW. Touch the loose wire with a finger and watch OUT follow your hum.
4. Wire the 74HC00 as above and repeat the four combinations. OUT is 5 V or 0 V (the 74HC output goes almost to the rails; the transistor version can only reach 0.2 V).
5. Threshold test: hold B = 1, connect input A of the 74HC00 to the wiper of a 10 kΩ pot across the supply and turn it while watching the LED. The output flips at about 2.5 V (half the supply). Do the same with the transistor gate: it flips at about 0.65 V (one base-emitter drop): a much worse noise margin.

Build 2: a 555 blinker clocking a flip-flop

The TLC555 oscillates at about 1 Hz; its output drives LED1 and also the clock of one 74HC74 flip-flop wired as a toggle, whose Q output drives LED2 at half the rate.

1. Power on. LED1 flashes about once a second, about equally on and off. LED2 flashes at half the rate, and changes state only at the moment LED1 turns on (the rising edge).
2. Count 20 flashes of LED1 with a stopwatch: about 19 s for the calculated 0.949 s each (anywhere from 15 to 25 s is normal with a 20 % capacitor).
3. Meter on the timing node (pin 2/6): about 2.5 V steady on a digital meter, the average of a signal swinging between 1.67 V and 3.33 V. Meter on OUT: about 2.5 V average (a rapidly switching signal reads its average).
4. Change C to 1 µF: the blinker runs ten times faster (10.5 Hz, too fast to count but a visible flicker); LED2 at 5.3 Hz.
5. Disconnect pin 2 (1D) from pin 6 and tie it to the + rail: LED2 stays on after the first clock edge, because D is always 1: a flip-flop remembers D at the clock edge.
6. Try the unused-input rule: disconnect pin 12 (2D) and pin 11 (2CP) from the rail. The second flip-flop is not connected to anything, but the supply current of the chip can rise and the chip warm slightly; floating inputs do harm even with no visible effect.

Build 3: PWM motor-speed control with the 555

Pulse-width modulation switches a motor fully on and fully off, thousands of times a second; the fraction of the time that it is on (the duty cycle D) sets the average voltage, and so the speed. The 555's duty cannot go below 50 % with the plain circuit, so two diodes steer the capacitor's charge and discharge currents through different parts of the potentiometer: moving the wiper trades charge time against discharge time while the total stays almost constant, so the frequency stays near-constant and only the duty changes.

1. Turn P1 fully towards end A (p = 0): LED1 almost off, the motor is stopped. Pin 3 average about 0.05 to 0.1 V (D about 1 to 2 %).
2. Turn it a quarter of the way (p = 0.25): LED1 dim; pin 3 reads about 1.7 V (D about 35 %); the motor is about to start (hobby motors need about 2 V average to overcome friction; the average at this position is 6 V × 35 % = 2.1 V).
3. Half way (p = 0.5): pin 3 about 3.0 V (D about 61 %), the motor runs at medium speed; three quarters: about 4.0 V (D about 82 %); fully towards B: LED1 full and the motor at full speed (pin 3 about 4.9 V).
4. Speed in relation to duty: motor speed is close to proportional to the average voltage D × 6 V above the stall point (the motor acts like a low-pass filter on the pulses: its winding inductance of a few mH and its inertia average the 3 kHz).
5. Remove D3 for a moment (power off first): the drain terminal shows spikes above 6 V when the MOSFET switches off the inductive load (the flyback voltage of Basic Electronics 5). With D3 in place the drain never exceeds about 6.7 V.
6. Compare the frequency at each position with a frequency meter or the simulator: it changes from about 3.2 kHz to 2.6 kHz as p goes from 0.25 to 0.75, not exactly constant, as the table predicts.

Simulators

Falstad Circuit Simulator (falstad.com/circuit): gates, flip-flops, counters and the 555 are in the Draw menu under the Logic Gates and Digital Chips groups (and the Circuits menu has ready-made 555 astable and flip-flop examples, a good place to start). For Build 1, draw two NPN transistors from Active Components, add logic-level inputs via Inputs and Sources (a logic input element) and use a 5 V source; Falstad's transistors are ideal enough to give the 0.2 V low and 5 V high of the calculation. For Build 2, drop a 555 chip with R1, R2 and C; a D flip-flop with Q-bar joined to D divides by two, and the scope shows both traces. For Build 3, model the motor as a 40 Ω resistor in series with a 5 mH inductor (6 V / 0.15 A = 40 Ω), put D3 across both, and use a logic-level N-channel MOSFET (a plain MOSFET with a 5 V gate is enough); put a slider on the potentiometer resistance and watch the duty cycle on the scope.

Tinkercad Circuits (tinkercad.com): the component list has a 555 timer, a 74HC595 shift register, LEDs, push buttons, a DC motor, a power supply, a multimeter and an oscilloscope, and an Arduino Uno. Tinkercad's list of logic ICs has changed over time, so search it for the 74-series chips (hex inverter, quad NAND and flip-flop); if one is missing, build the same function from the transistors or use Falstad for that chip. Its 555 follows the same formulas; set R₁, R₂ and C and measure the output with the oscilloscope, which gives the period and duty directly. A 74HC595 with an Arduino and the shiftOut() function is a good simulation of the three-pin expansion of section 8.

Expected readings

Real readings spread because the capacitor in Build 2 is a ±20 % part, diodes differ, the 555 has a timing error of a few percent and an LED's voltage varies between colours and batches. What does not vary is the structure: the transistor NAND is LOW only when both inputs are HIGH; the 74HC switches near half the supply and the transistor gate near 0.65 V; LED2 changes only on the rising edge of LED1 and runs at exactly half its rate; and in Build 3 the duty (and so the speed) rises as the wiper moves away from the D1 end while the frequency stays within about 20 % of 3 kHz.

13. Challenges

Next, Basic Electronics 9 moves from signals to power: DC motors, servos and steppers at circuit level, H-bridge and motor-driver chips, relays, and the batteries, regulators and current budgets that keep a robot from browning out. The PWM idea of Build 3 returns there in a full H-bridge.