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bi-quinary

The most efficient way of performing computations by means of digital computing is to use binary, but when numbers have to be input from and displayed to human beings, we usually need decimal notation and that requires a conversion that can sometimes be expensive.

Early computers often used BCD (Binary Coded Decimal), where each decimal digit is stored on a group of 4 bits called a “nibble”, but I recently learned about yet another way of storing numbers for convenient input and output: the bi-quinary.

This system stores a decimal digit as a binary number paired with a “quinary” number. A binary number has two states, a quinary number has five. Think of it as a group of 5 bits where only one bit can be on at any time.

The very first mass-produced computer, the IBM 650 from 1953, used bi-quinary numbers. You should definitely check its web page on the IBM archives (link), and have a look at the pictures where you can actually see the console unit front panel. See those groups of seven lights in Y shapes? Close up view here: (link).

The one binary number controls the two lights above, the five vertical lights being the quinary number. If the left light is on, the vertical lights read 0 1 2 3 4, if the right one is on they read 5 6 7 8 9. In a sense, those machines where computing in base 5. That, together with the fact they look so cool makes me totally want one. Honey, we still have a bit of free space in that room, right?

By the way, if you have five fingers, you have sort of an IBM 650 emulator “at hand”. Learn “Chisenbop” and discover a new way of counting on your fingers: (link).