BCD and Gray Code

BCD: 59 → 0101 1001. Used by real-time-clock chips and 7-segment displays.

Gray code: consecutive values differ by exactly one bit, so a reading taken mid-transition is never wildly wrong — used in rotary encoders and to pass counters between clock domains.

$G = B \oplus (B \gg 1)$

Decimal	Binary	Gray
0	000	000
1	001	001
2	010	011
3	011	010
4	100	110