BCD.DAY
Where every digit finds its binary home.
THE CONVERSION
THE MACHINE ROOM
Humans count in tens. It is an accident of anatomy -- ten fingers, ten digits, a decimal system that has survived every revolution in mathematics for five thousand years. When we write "42," we see a quantity, an idea, a meaning. The symbol is transparent to us.
But machines have no fingers. They have switches. On or off. One or zero. The entire edifice of digital computing rests on this brutal simplification: everything must be expressed in binary. The question that haunted early engineers was not "can we compute?" but "how do we translate?"
Binary-Coded Decimal was the answer. Each decimal digit is encoded independently into 4 binary bits. No complex conversion. No floating-point ambiguity. A direct, digit-by-digit mapping between the human world and the machine world.
42 (decimal)
0100 0010 (BCD)
00101010 (pure binary)
In BCD, each digit keeps its identity. 4 becomes 0100. 2 becomes 0010. The human meaning survives the translation intact.
In pure binary, the meaning dissolves into efficiency. 42 becomes 00101010 -- a number that has no visible relationship to the decimal original. Faster for machines. Illegible to humans.
BCD chose fidelity over efficiency.
THE REGISTER
8421 BCD
5 = 0101The natural BCD. Weight positions mirror powers of two.
Excess-3
5 = 1000Add 3 to each digit before encoding. Self-complementing.
2421 Code
5 = 1011Weighted code with digit complement symmetry.
Gray Code
5 = 0111Only one bit changes between adjacent values.
Aiken Code
5 = 10112-4-2-1 weighted. Self-complementing like Excess-3.
Stibitz Code
5 = 1000Used in relay-based computers of the 1940s.
COMP-3
+123 = 123CPacked decimal. Two digits per byte. Sign in last nibble.
Chen-Ho
3 digits = 10 bitsDense BCD. Encodes three digits in ten bits.
THE LEGACY
ENIAC uses decimal ring counters. Each digit stored as 10 vacuum tube flip-flops. BCD is implicit in the hardware architecture itself.
IBM 1401 makes packed decimal the standard for business computing. COBOL adopts COMP-3 format. Every bank balance is stored in BCD.
Intel 8086 includes DAA and DAS instructions for BCD arithmetic. The x86 architecture carries BCD support into the modern era.
IEEE 754-2008 adds decimal floating-point formats. DPD encoding stores three decimal digits in ten bits. BCD principles endure.
Financial systems, mainframes, calculator chips, and tax software still rely on decimal arithmetic. Where precision matters, BCD persists.