Decimal to BCD converter
Convert a decimal number to Binary-Coded Decimal by encoding each digit into its own 4-bit binary group, with every digit shown separately.
How it works
BCD does not convert a number to binary. It converts each
digit to binary, separately, and keeps them in order — so 2026
becomes four independent 4-bit groups rather than one binary number. That is why
the two outputs above disagree: as plain binary 2026 is
11111101010, but as BCD it is four groups that still
visibly read 2, 0, 2, 6. Four bits can hold sixteen values while a digit only needs
ten, so the six patterns from 1010 to
1111 are simply never used — wasteful, and
deliberately so. The payoff is that driving a seven-segment display, or printing a
number, needs no division at all: each group already is the digit. That trade
mattered enough that BCD is still in calculators, digital clocks, and financial
systems where decimal rounding has to behave exactly as a person expects.