AP CSP Big Idea 2 (Data): From Bits to Meaning

Binary

A number system that uses only two symbols (0 and 1) to represent all data, matching the two reliable physical states in computer hardware.

Bit

A single binary digit (0 or 1); the basic unit of data in computing.

Byte

A group of 8 bits.

Bit Patterns (2^n possibilities)

With n bits, there are 2^n different possible bit patterns, allowing representation of that many distinct values (numbers, characters, colors, etc.).

Base-2 Positional Number System

A positional number system where each digit position represents a power of 2 (instead of powers of 10 as in decimal).

Place Value (Powers of 2)

In binary, positions from right to left have values 2^0, 2^1, 2^2, 2^3, … and a binary number equals the sum of place values where the bit is 1.

Range (Unsigned n-bit Integer)

For n bits used to store a nonnegative integer, the minimum is 0 and the maximum is 2^n − 1.

Overflow

An error/limit condition when a value is too large to fit in the available number of bits, causing an incorrect stored pattern (e.g., wrap-around depending on the system).

Encoding

An agreed-upon mapping that assigns meaning to bit patterns (e.g., interpreting bits as numbers, text characters, pixel colors, or audio samples).

Resolution (Image)

The number of pixels in an image (width × height). Higher resolution means more pixels and typically larger file size.

Color Depth

The number of bits used per pixel; determines how many distinct colors/values a pixel can represent (2^b for b bits per pixel).

Sample Rate

In digital audio, the number of samples captured per second (how often the sound amplitude is measured).

Bit Depth (Audio)

The number of bits used per audio sample, controlling the precision of each amplitude measurement; higher bit depth usually means higher potential accuracy and larger data size.

Data Compression

The process of encoding information using fewer bits than the original representation to save storage and/or transmission time.

Lossless Compression

Compression that preserves all original information; decompression reproduces the exact original data.

Lossy Compression

Compression that permanently removes some information (often less noticeable to humans) to reduce file size; decompression cannot perfectly restore the original.

Redundancy

Repeated or predictable patterns in data that can be exploited by lossless compression to reduce the number of bits needed.

Run-Length Encoding (RLE)

A lossless compression method that replaces repeated sequences with a value and a count (e.g., “8 ones, 5 zeros”)—works best with long runs.

Dictionary-Based Compression

A lossless method that builds a dictionary of repeated sequences and replaces them with shorter references, storing enough info to reconstruct the original exactly.

Data Cleaning

Preparing raw data for analysis by fixing missing/incorrect values, correcting formats, removing duplicates, standardizing categories/units, and filtering irrelevant records.

Aggregation (Summary Statistics)

Combining many data values into summaries such as counts, totals, averages, minimums, or maximums; useful but can hide variation.

Outlier

An unusual data value that may indicate an error or an important rare event; should be investigated rather than automatically removed.

Metadata

Data about data that provides context for interpretation (e.g., timestamps, units, column descriptions, photo location/camera info) and can raise privacy concerns.

Correlation vs. Causation

Correlation means two variables change together; causation means one directly produces a change in the other. Correlation alone does not prove causation.

Sampling Bias

A bias that occurs when a sample is not representative of the population because certain groups are systematically excluded or underrepresented.