Countdown timer on a four-digit display, on an Arduino Uno

// A countdown timer: set it with two buttons, start it with a third.
//
//   74HC595 DS -> pin 8    SHCP -> pin 13    STCP -> pin 12
//   Q0 to Q7 -> segments a to g and the dot of a four-digit display
//   digit commons DIG1 to DIG4 -> pins 2, 3, 4, 5 (LOW lights a digit)
//   "minute" button  -> A3, to GND    "second" button -> pin 6, to GND
//   "function" button -> A1, to GND   (all three on INPUT_PULLUP)
//   LED -> A0, through 220 ohm        buzzer -> A2 (through a transistor on the bench)
//
// The four digits share their segment lines, so the sketch lights one digit
// at a time, a few milliseconds each, round and round: fast enough that you
// see all four at once. That is multiplexing, and it is why the display code
// runs on every pass of loop() and nothing in loop() may delay() for long.
//
// Press "minute" to add a minute and "second" to add a second. Press
// "function" to start; press it again to clear. When the time runs out the
// buzzer sounds and the LED flashes until you press "function".
//
// The analog pins work as ordinary digital pins: A0 to A5 are pins 14 to 19.

const int DATA_PIN = 8;
const int LATCH_PIN = 12;
const int CLOCK_PIN = 13;
const int DIGIT_PINS[4] = {2, 3, 4, 5};
const int BUTTON_MINUTE = A3;
const int BUTTON_SECOND = 6;
const int BUTTON_FUNCTION = A1;
const int LED = A0;
const int BUZZER = A2;

//                   gfedcba
const byte DIGITS[10] = {0x3F, 0x06, 0x5B, 0x4F, 0x66, 0x6D, 0x7D, 0x07, 0x7F, 0x6F};

enum State { SETTING, RUNNING, RINGING };
State state = SETTING;
long remaining = 0;  // seconds
unsigned long lastTick = 0;
int digit = 0;

struct Button {
  int pin;
  bool down;
  unsigned long changedAt;
};
Button buttons[3] = {{BUTTON_MINUTE, false, 0}, {BUTTON_SECOND, false, 0}, {BUTTON_FUNCTION, false, 0}};

// True once per press, after the contact has settled for 30 ms.
bool pressed(Button &b) {
  bool now = digitalRead(b.pin) == LOW;
  if (now != b.down && millis() - b.changedAt > 30) {
    b.down = now;
    b.changedAt = millis();
    return now;
  }
  return false;
}

void showDigit(int which, byte pattern) {
  for (int i = 0; i < 4; i++) digitalWrite(DIGIT_PINS[i], HIGH);
  digitalWrite(LATCH_PIN, LOW);
  shiftOut(DATA_PIN, CLOCK_PIN, MSBFIRST, pattern);
  digitalWrite(LATCH_PIN, HIGH);
  digitalWrite(DIGIT_PINS[which], LOW);
}

void refresh() {
  int minutes = remaining / 60;
  int seconds = remaining % 60;
  byte patterns[4] = {DIGITS[minutes / 10 % 10], (byte)(DIGITS[minutes % 10] | 0x80), DIGITS[seconds / 10],
                      DIGITS[seconds % 10]};
  showDigit(digit, patterns[digit]);
  digit = (digit + 1) % 4;
}

void printTime() {
  Serial.print(remaining / 60);
  Serial.print(remaining % 60 < 10 ? ":0" : ":");
  Serial.println(remaining % 60);
}

void setup() {
  pinMode(DATA_PIN, OUTPUT);
  pinMode(LATCH_PIN, OUTPUT);
  pinMode(CLOCK_PIN, OUTPUT);
  for (int i = 0; i < 4; i++) pinMode(DIGIT_PINS[i], OUTPUT);
  pinMode(BUTTON_MINUTE, INPUT_PULLUP);
  pinMode(BUTTON_SECOND, INPUT_PULLUP);
  pinMode(BUTTON_FUNCTION, INPUT_PULLUP);
  pinMode(LED, OUTPUT);
  pinMode(BUZZER, OUTPUT);
  Serial.begin(9600);
  Serial.println("Mokxi Uno: countdown timer. minute (A3) and second (6) set it, function (A1) starts it.");
  // Something to count down from straight away, so it is not a blank display.
  remaining = 5;
  state = RUNNING;
  lastTick = millis();
  Serial.println("start: 0:05");
}

void loop() {
  bool minute = pressed(buttons[0]);
  bool second = pressed(buttons[1]);
  bool function = pressed(buttons[2]);

  if (state == SETTING) {
    if (minute && remaining < 99L * 60) remaining += 60;
    if (second && remaining < 99L * 60 + 59) remaining += 1;
    if (minute || second) printTime();
    if (function && remaining > 0) {
      state = RUNNING;
      lastTick = millis();
      Serial.println("start");
    }
  } else if (state == RUNNING) {
    if (function) {
      state = SETTING;
      remaining = 0;
      Serial.println("cleared");
    } else if (millis() - lastTick >= 1000) {
      lastTick += 1000;
      remaining--;
      printTime();
      if (remaining <= 0) {
        remaining = 0;
        state = RINGING;
        Serial.println("time is up");
      }
    }
  } else {
    bool on = (millis() / 250) % 2 == 0;
    digitalWrite(LED, on ? HIGH : LOW);
    digitalWrite(BUZZER, on ? HIGH : LOW);
    if (function) {
      state = SETTING;
      digitalWrite(LED, LOW);
      digitalWrite(BUZZER, LOW);
      Serial.println("quiet");
    }
  }

  refresh();
  delay(3);
}