AP® Computer Science Principles · Big Idea 2 · Topic 2.1

Bits, Bytes, and Representing Everything Digitally

A bit is one on/off switch, the smallest unit of information. Group bits together and their combinations can stand for numbers, letters, or colors — which is how all digital data, from texts to photos, reduces to nothing but zeros and ones.

A computer is built from switches that are either on or off. Nothing in between. One switch, two possible states, is exactly what a bit is: the smallest unit of information, just enough to tell two things apart. On its own a single bit is not very useful — it can only mean yes or no, true or false, 0 or 1. The power comes from grouping bits. Line up eight of them and you get a byte, and now you are not choosing between 2 things but between 256, because each extra bit doubles how many combinations exist.

That doubling is the whole trick. One bit gives 2 values, two bits give 4, three give 8, four give 16. In general n bits give 2n distinct values, since every new switch can be paired with on or off against every combination that already existed. A byte, with its 256 combinations, is enough to assign a unique pattern to every letter, digit, and punctuation mark in a text encoding, or to represent 256 shades of gray in a black-and-white photo. The pattern itself carries no built-in meaning — 01000001 is just eight switches set a certain way. Software agrees on a scheme ahead of time, so that same pattern is read as the number 65, or the letter A, or a particular shade, depending on context.

This is the foundation under everything else in representing data digitally. Colors mix bytes for red, green, and blue; sound samples amplitude many times a second into bits; images arrange pixels, each one a number, into a grid. All of it traces back to switches that are only ever on or off, counted in groups to represent something a person recognizes.

Key terms

bit
The smallest unit of digital information, distinguishing exactly two states, usually written 0 or 1.
byte
A group of eight bits, capable of representing 28 = 256 distinct values.
binary
A number system using only two digits, 0 and 1, matching the two states a switch can hold.
encoding
An agreed-upon scheme for what a particular pattern of bits is meant to represent, such as a letter or color.

Watch it explained

  1. How it worksHow do eight bits grouped into a byte become a number, a letter, or a shade of gray?
  2. How it worksWalk me through how one physical switch being on or off carries exactly one bit of information.
  3. Worked exampleFind how many different values 4 bits can represent, and list every one of them.
  4. Going furtherWhat happens to the count of possible values each time you add one more bit?

Check yourself

Your turn1 of 2
A digital sensor uses 15 on/off switches to encode information. How many distinct values can it represent using all 15 switches?

End of topic.