Digital logic and microcontrollers

Why it matters

Almost every electrical product now has a microcontroller in it: chargers, inverters, motor drives, protective relays, meters, sensors. Electrical engineers write firmware, read logic analyser traces and design the interface between digital pins and real loads. Underneath all of it are a few gates and the idea of a registerA row of flip-flops sharing a clock, such as 8 or 32 bits, often wired to hardware in an MCU.: a row of bits, each one wired to something.

Logic levels and gates

Digital circuits treat a voltage as 1 (high) or 0 (low). A 3.3 V CMOS input typically reads anything above about 2 V as 1 and below about 0.8 V as 0; the band in between is undefined. Mixing 5 V and 3.3 V parts needs care: a 5 V output can damage a 3.3 V input that isn't "5 V tolerant", so you use a level shifter or a divider.

The basic gates and their truth tables:

A B | AND OR XOR NAND
0 0 |  0   0   0    1
0 1 |  0   1   1    1
1 0 |  0   1   1    1
1 1 |  1   1   0    0
NOT: 0 -> 1, 1 -> 0

NAND (and NOR) is universal: any logic function can be built from NAND gates alone. Inside a chip, each gate is a few CMOS transistors used as the switches from the previous lessons.

Combinational logic: adding numbers

A half adder adds two bits: sum = A XOR B, carry = A AND B. A full adderA logic circuit that adds two bits and a carry in, giving a sum bit and a carry out. also takes a carry in:

sum  = A XOR B XOR Cin
Cout = (A AND B) OR (Cin AND (A XOR B))

Chain four full adders, passing each carry to the next, and you have a 4-bit ripple-carry adder. 0101 (5) + 0011 (3) gives 1000 (8). The output depends only on the present inputs, which is what "combinational" means.

Sequential logic: memory

A flip-flopA circuit that stores one bit; a D flip-flop copies D to Q on each rising clock edge. stores one bit. A D flip-flop copies its D input to its Q output on each rising clock edge and holds it until the next edge. A register is a row of flip-flops sharing a clock, for example 8 or 32 bits. Counters, shift registers and the state machines in every controller are built from registers plus combinational logic. The clock sets the pace: the logic between registers must settle within one clock period.

Inside a microcontroller

A microcontroller (MCU) puts a CPU, flash memory for the program, RAM, and peripherals on one chip: GPIO, timers, PWM, ADCs, UART, SPI and I2C. Peripherals are controlled through memory-mapped registers: writing a number to a particular address changes the hardware.

GPIO (general-purpose input/output) pins are usually configured with registers like:

• a direction register (bit = 1 for output),
• an output register (bit = 1 drives the pin high),
• an input register (read the pin's level).

You change one pin without disturbing the others with bit masksNumbers like 1 << n combined with |, & and ~ to change or read one bit without disturbing the others.:

REG |=  (1 << 5);        // set bit 5   (pin 5 high)
REG &= ~(1 << 5);        // clear bit 5 (pin 5 low)
int on = (REG >> 5) & 1; // read bit 5
REG ^=  (1 << 5);        // toggle bit 5

Arduino's digitalWrite(pin, HIGH) does exactly this behind the scenes.

Worked example. A port register holds 0b00010010 (pins 1 and 4 high). Setting bit 0 gives 0b00010011 (19); then clearing bit 4 gives 0b00000011 (3). Reading bit 1 gives 1.

Pins meet the real world

• Current limits: a GPIO pin can source or sink only a few to about 20 mA, and the whole port has a total limit. Use a transistor (previous lesson) for anything bigger.
• Pull-upA resistor that holds an input high when nothing drives it, so it does not float. and pull-down resistors keep an input from floating when a button is open. Many MCUs have internal pull-ups you enable in a register.
• DebouncingWaiting or sampling repeatedly so the few milliseconds of switch bounce are not read as several presses.: mechanical switches bounce for a few milliseconds, so firmware waits or samples repeatedly before accepting a change.
• Interrupts let the CPU react to an edge immediately instead of polling.

Simulate it

Wokwi (https://wokwi.com) simulates Arduino and other boards in the browser, with LEDs, buttons and a logic analyser. Logic simulators such as Logisim Evolution let you build adders from gates. No hardware is needed.

Common mistakes

• Writing the whole register (REG = 1 << 5) and accidentally turning every other pin off.
• Forgetting the NOT when clearing: REG &= (1 << 5) clears everything except bit 5.
• Floating inputs with no pull-up, giving random readings.
• Driving loads straight from a pin beyond its current rating.
• Connecting 5 V signals to 3.3 V-only inputs.

Recap

• Gates implement Boolean logic; NAND is universal; full adders chain into multi-bit adders.
• Flip-flops and registers store state on clock edges.
• MCUs control peripherals through registers; use |=, &= ~ and shifts to change single bits.

Try it

Open the Do tab to build a full adder, a 4-bit adder and GPIO bit helpers in JavaScript.