Binary serial numbers
A binary serial uses only two distinct digits — 74774774. There are 11,430 in a run of 99,999,999. The 254 that use only 0 and 1 are the ones people actually pay for.
Working out the count
Pick two digits out of ten — there are C(10,2) = 45 such pairs. For each pair, an eight-digit string can be built 28 = 256 ways, less the two that use only one of the digits, leaving 254. So 45 × 254 = 11,430, or one note in 8,749.
Restrict the pair to 0 and 1 and only one of those 45 pairs qualifies: 254 serials, one note in 393,701. Forty-five times scarcer, and worth a good deal more than forty-five times as much attention, because a serial made of 0s and 1s is something anyone recognises on sight.
The binary family
| Pattern | Example | In a run | Odds | Standing |
|---|---|---|---|---|
| True binary radar Palindrome using only 0 and 1. Fourteen exist in a full run, which is solid-and-ladder territory. | 10100101 | 14 | 1 in 7,142,857 | Trophy |
| Binary radar repeater Palindrome and repeater at once, on two digits. | 61166116 | 90 | 1 in 1,111,111 | Major |
| True binary Only 0s and 1s. The "looks like code" appeal makes these marketable. | 10110010 | 254 | 1 in 393,701 | Mid-market |
| Binary radar Palindrome using only two digits. | 83833838 | 630 | 1 in 158,730 | Mid-market |
| Binary Exactly two distinct digits. | 74774774 | 11,430 | 1 in 8,749 | Entry fancy |
| Trinary Exactly three distinct digits. At 1 in 143 this is not rare — usually face value. | 79557977 | 695,520 | 1 in 144 | Face value |
What one is worth
Premiums are added to face value rather than multiplied by it, and they fall away fast with handling — these are uncirculated figures. A folded example keeps well under half of this.
| Pattern | $1 note | $20 note | $100 note |
|---|---|---|---|
| True binary radar | $250 – $3,000 | $475 – $5,400 | $750 – $7,900 |
| Binary radar repeater | $60 – $400 | $130 – $750 | $250 – $1,100 |
| True binary | $16 – $90 | $45 – $180 | $140 – $325 |
| Binary radar | $16 – $90 | $45 – $180 | $140 – $325 |
| Binary | $4 – $25 | $25 – $65 | $110 – $165 |
| Trinary | $1 | $20 | $100 |
Check a serial for collector patterns — the checker tests all 34 patterns at once and reports every one a serial matches, with the odds for each.
The trinary trap
A trinary uses exactly three distinct digits, and it is the most over-reported pattern in the hobby. There are 695,520 per run — one note in 144, which is roughly one in every strap of notes. It has a name and a definition, and it does not have buyers. Our checker reports it as a fact rather than as a find.
Questions
What is a binary serial number?
A serial that uses only two distinct digits across all eight positions, like 74774774. A stricter definition, and the one that carries the premium, requires those two digits to be 0 and 1 — a true binary, like 10110010, which looks like machine code.
How rare is a binary note?
Choose two digits from ten and any arrangement using both: C(10,2) x (2^8 - 2) = 45 x 254 = 11,430 per run, or one note in 8,749. True binaries using only 0 and 1 are just the 254, or one in 393,700.
Why are true binaries worth more?
Partly scarcity — 254 against 11,430 — and mostly appearance. A serial of 0s and 1s reads as code, which is instantly recognisable and easy to describe in a listing. Recognisability drives price in this hobby at least as much as rarity does.
Is a trinary worth anything?
Almost never. A trinary uses exactly three distinct digits, and there are 695,520 per run — one note in 144. Roughly one banknote in every strap of 150 is a trinary. It has a name, which is not the same as having a market.
What is a binary radar?
A serial that is both a palindrome and uses only two digits. There are 630 per run. If it also reads the same as a repeater it is a binary radar repeater, and if the two digits are 0 and 1 it is a true binary radar — of which just fourteen exist in a full run.