Digital/analog signals, Gray and Excess-3 codes

Analog signal

An analog signal is a continuous signal that can take any value within a range at every instant of time, e.g. a sine wave, voice from a microphone, or temperature from a thermocouple.

Digital signal

A digital signal takes only a finite number of discrete values (usually two: 0 and 1) and changes only at discrete instants, e.g. the clock or data in a computer.

 Analog :   /\    /\        Digital:  _   __    _
           /  \  /  \                | | |  |  | |
          /    \/    \             __| |_|  |__| |__

Gray code

Gray code is an unweighted, reflected binary code in which consecutive numbers differ in only one bit.

Binary to Gray: keep MSB, then $G_i = B_{i+1} \oplus B_i$. Example: $(1011)_2$ → 1, 1⊕0 = 1, 0⊕1 = 1, 1⊕1 = 0 → $(1110)_{Gray}$. Used in shaft encoders and K-maps.

Excess-3 code

Excess-3 is an unweighted BCD code where each decimal digit is coded as the binary of digit + 3.

Example: $(27)_{10}$ → 2+3 = 5 → 0101, 7+3 = 10 → 1010 → $(0101\ 1010)_{XS-3}$. It is self-complementing: inverting the bits gives the 9's complement (e.g. 2 = 0101 → 1010 = 7 = 9 − 2).