Bit

A bit is the fundamental unit of information in computers. It represents a choice between two values: usually written as 0 and 1.

In computers, a bit represents an on-off state, and we can combine multiple bits to make larger units of information, such as a nibble or byte.

A bit is a binary digit.

Number of values represented by bits

n bits can represent 2^n different values.

For example:

• 1 bit can represent 2 values: 0 or 1.
• 2 bits can represent 4 values: 00, 01, 10, or 11.
• 3 bits can represent 8 values: 000, 001, 010, 011, 100, 101, 110, or 111.
• 4 bits can represent 16 values: 0000 to 1111.
• And so on.

This is because each bit can be in one of two states, and the total number of combinations is 2^n.

Number of bits needed for values

We can also go in reverse (assuming we know how to calculate logarithms):

• To represent m different values, we need at least \log_2 m bits.
• For example:
  • To represent 32 values, we need at least \log_2 32 = 5 bits.
  • To represent a full RGB color (16,777,216 values), we need at least \log_2 16777216 = 24 bits. (that’s why it’s called “24-bit color”).

Common multiples of bits

• Most systems use a 64-bit instruction set architecture nowadays, meaning they process data in chunks of 64 bits at a time.
• Another common size is 32-bit, which was widely used in older systems and in windows programs which are still using ancient technology - typical windows ;)