Binary data
These are often labelled as 0 and 1 in accordance with the binary numeral system and Boolean algebra.
A discrete variable that can take only one state contains zero information, and 2 is the next natural number after 1.
That is why the bit, a variable with only two possible values, is a standard primary unit of information.
A collection of n bits may have 2n states: see binary number for details.
10k bits are more than sufficient to represent an information (a number or anything else) that requires 3k decimal digits, so information contained in discrete variables with 3, 4, 5, 6, 7, 8, 9, 10... states can be ever superseded by allocating two, three, or four times more bits.
Boolean functions are also well-studied theoretically and easily implementable, either with computer programs or by so-named logic gates in digital electronics.
This contributes to the use of bits to represent different data, even those originally not binary.
For example, binary data is often used to represent the party choices of voters in elections in the United States, i.e. Republican or Democratic.
Like all discretization, it involves discretization error, but the goal is to learn something valuable despite the error: treating it as negligible for the purpose at hand, but remembering that it cannot be assumed to be negligible in general.
When this is grouped, the values are added, while the number of trial is generally tracked implicitly.
the total number of trials (points in the grouped data).
categorical variables with more than two categories can be modeled with a multinomial regression.
In modern computers, binary data refers to any data represented in binary form rather than interpreted on a higher level or converted into some other form.
At the lowest level, bits are stored in a bistable device such as a flip-flop.
Computers rarely modify individual bits for performance reasons.
The "text" vs. "binary" distinction can sometimes refer to the semantic content of a file (e.g. a written document vs. a digital image).
