Code: Let's Build a Clock!

In one line: a clock is just counters — divide a fast oscillator down to one tick per second, count 0–59, reset, carry into minutes and hours, and decode the digits for a display.

Companion to: Charles Petzold, Code (2nd edition), chapter 18.

Binary-coded decimal (BCD)

Each decimal digit gets its own 4 bits, so displays are easy to drive.

Decimal	BCD
5	`0101`
9	`1001`
59	`0101 1001` (5 and 9 stored separately)
12	`0001 0010`

Codes 1010–1111 go unused in BCD, so a counter must reset to 0 after 9.

Counting time

Stage	Counts	Resets when
Seconds (ones digit)	0–9	It passes 9 → carries into the tens digit
Seconds (tens digit)	0–5	It reaches 6 → carries into minutes
Minutes	00–59	Same pattern
Hours	1–12	Past 12 → back to 1; AM/PM toggles at 12

Detecting “reached 6” or “passed 9” is a job for a few gates watching the counter’s bits.

Getting 1 Hz

Quartz watch and PC clock crystals typically run at 32,768 Hz = 2¹⁵. Fifteen divide-by-two flip-flops bring that down to exactly 1 Hz.

Seven-segment displays

  aaa
 f   b
 f   b
  ggg
 e   c
 e   c
  ddd

Digit	Segments lit
0	a b c d e f
1	b c
2	a b d e g
3	a b c d g
4	b c f g
5	a c d f g
6	a c d e f g
7	a b c
8	a b c d e f g
9	a b c d f g

A decoder — gates, or a small ROM — turns each 4-bit BCD digit into these seven on/off signals.

Try it

' '.join(f'{int(d):04b}' for d in "59")   # '0101 1001' — BCD for 59
2**15                                     # 32768

w32tm /query /status          # Windows time source and last sync

timedatectl                   # Linux clock, time zone and NTP status

🔐 Security and IT connections

Every PC has this clock inside. The real-time clock chip runs on a 32.768 kHz crystal, kept alive by the CMOS battery — which is why a dead coin cell resets the date.
Time is a security control:
- Kerberos (Active Directory logons) rejects clocks more than 5 minutes apart by default.
- TLS certificates fail outside their validity dates.
Log correlation needs synchronised clocks. Keep systems on NTP and store logs in UTC; a timeline is useless if every machine disagrees about the time.

Practice drills

1. Write 47 in BCD.

0100 0111

2. Which segments light for the digit 7?

a, b and c.

3. A domain PC suddenly can't log users in and its clock is 20 minutes fast. Why?

Kerberos rejects the time skew (default limit 5 minutes). Resync with w32tm /resync.

Key takeaways

BCD stores each decimal digit in 4 bits — handy for displays.
Counters plus reset logic count seconds, minutes and hours; dividers turn a fast crystal into 1 Hz.
Seven-segment decoders map digits to segments.
Accurate time underpins authentication, certificates and log timelines.