Verified Mathematical Proofs
Open Interactive ConverterFive Key Times of Day Worked Out
Step-by-step bit breakdowns for Standard Binary and BCD across benchmark timestamps.
Example 1: Afternoon Benchmark (13:45:09)
Classic Textbook ExampleStandard Binary (Base-2)
Hours (13):
01101 → 8 + 4 + 1 = 13Minutes (45):
101101 → 32 + 8 + 4 + 1 = 45Seconds (09):
001001 → 8 + 1 = 9BCD (4-Bit Nibbles)
Hours:
0001 (1) • 0011 (3)Minutes:
0100 (4) • 0101 (5)Seconds:
0000 (0) • 1001 (9)Example 2: Midnight Rollover (00:00:00)
Zero State BoundaryStandard Binary (Base-2)
Full String:
00000 : 000000 : 000000All 17 bits are completely off (0)
BCD (4-Bit Nibbles)
Full String:
0000 0000 : 0000 0000 : 0000 0000All 24 nibble bits are inactive (0)
Example 3: Midday / Noon (12:00:00)
Half-Day BenchmarkStandard Binary (Base-2)
Hours (12):
01100 (8 + 4 = 12)Minutes (00):
000000Seconds (00):
000000BCD (4-Bit Nibbles)
Hours:
0001 (1) • 0010 (2)Minutes:
0000 (0) • 0000 (0)Seconds:
0000 (0) • 0000 (0)Example 4: Upper Boundary (23:59:59)
Maximum Active BitsStandard Binary (Base-2)
Hours (23):
10111 (16 + 4 + 2 + 1)Minutes (59):
111011 (32 + 16 + 8 + 2 + 1)Seconds (59):
111011 (32 + 16 + 8 + 2 + 1)BCD (4-Bit Nibbles)
Hours:
0010 (2) • 0011 (3)Minutes:
0101 (5) • 1001 (9)Seconds:
0101 (5) • 1001 (9)Binary Clock Examples FAQ
Why does 00:00:00 have no active bits?
In binary, zero is represented by all bits set to 0. At midnight, every indicator across hours, minutes, and seconds is turned off.
What is the maximum number of active bits at 23:59:59?
In Standard Binary, 23 (10111) has 4 bits, 59 (111011) has 5 bits, and 59 seconds has 5 bits, totaling 14 active bits out of 17. In BCD, 23:59:59 lights up 11 bits.
Can I convert other arbitrary times into binary?
Yes, you can use our interactive Binary Time Converter at /binary-time-converter/ to calculate and test any time of day instantly.