Big Idea 2: Data

Binary number

A base-2 number system that represents values using only the digits 0 and 1.

Bit

A binary digit; the smallest unit of information in a computer, representing one of two states (0 or 1).

Byte

A group of 8 bits; a common unit of storage and memory (256 possible bit patterns).

Bit pattern

A specific sequence of bits (like 0101) used to represent data such as numbers, text codes, pixel colors, or audio samples.

Binary place value

The idea that each bit position in a binary number represents a power of 2, increasing from right to left.

Binary value formula

A way to compute a binary number’s value: value = Σ(bi · 2^i), where each bi is 0 or 1.

Binary-to-decimal conversion

Converting by adding the powers of 2 corresponding to every bit position that contains a 1.

Decimal-to-binary conversion (repeated division)

Convert by repeatedly dividing by 2, recording remainders, and reading the remainders from last to first.

Decimal-to-binary conversion (powers-of-2 method)

Convert by subtracting the largest power of 2 that fits, repeating until 0, and marking 1s/0s for used/skipped powers.

Fixed number of bits

A storage constraint where a value must fit into a predetermined number of bits, limiting what can be represented.

2^n possible patterns

With n bits, a computer can represent exactly 2^n distinct bit patterns.

Unsigned integer range

When n bits represent nonnegative integers, the values range from 0 to 2^n − 1.

Overflow

An error-like situation where the true result needs more bits than available, causing the stored result to wrap or become incorrect.

Floating-point representation

A common computer method for representing real numbers (like scientific notation) that often requires rounding and can’t represent many fractions exactly.

Character encoding

A standard mapping that assigns characters (letters, digits, punctuation, etc.) to numeric codes so they can be stored as bits.

ASCII

An older character encoding standard designed mainly for basic English characters, mapping them to numeric codes.

Unicode

A broad character encoding standard designed to represent characters from many writing systems worldwide (much larger than ASCII).

Encoding mismatch

When systems interpret the same bits using different encodings, producing incorrect or garbled characters.

Bits per character

How many bits (or bytes) an encoding uses to store a character; this can vary by encoding and affects storage size.

Pixel

A “picture element”; one small square in a digital image grid, with its color stored as bits.

Raster image

An image represented as a grid of pixels arranged in rows and columns (common for photos and screenshots).

Resolution (image dimensions)

The width and height of an image measured in pixels (e.g., 1920×1080), affecting detail and file size.

Color depth (bits per pixel)

The number of bits used to store each pixel’s color; higher color depth allows more colors but increases file size.

RGB color model

A method for representing screen colors by mixing red, green, and blue light values (often stored as numbers).

Metadata

“Data about data”; extra information needed for interpretation or organization (e.g., image dimensions, units in a data set, timestamps).

Uncompressed image size formula

Approximate size (ignoring metadata/compression): bits = width · height · bitsPerPixel; bytes = bits/8.

Analog signal

A continuous signal over time with a continuous range of values (like real-world sound waves).

Sampling

Recording an analog signal at regular time intervals to create a digital representation made of discrete measurements.

Sampling rate

How many samples are taken per second (Hz); higher sampling rates usually improve accuracy but increase data size.

Bit depth (audio)

The number of bits used to store each audio sample; higher bit depth allows more amplitude levels and usually less error.

Quantization

The process of mapping sampled analog values to one of a limited set of digital levels, which can introduce rounding/quantization error.

Uncompressed audio size formula

Approximate size (ignoring metadata/compression): bits = seconds · samplesPerSecond · bitsPerSample · channels.

Data compression

Techniques that reduce the number of bits needed to store or transmit data by changing its representation.

Lossless compression

Compression that allows the original data to be reconstructed exactly from the compressed version (important for text and code).

Lossy compression

Compression that permanently discards some information to achieve smaller files, producing an approximation (common for JPEG/MP3/video).

Run-length encoding (RLE)

A simple lossless method that compresses repeated sequences by storing a value and its count (e.g., A5 B3 C2).

Compression ratio

A comparison of compressed size to original size; higher compression ratios mean greater size reduction.

Compression tradeoff

The idea that reducing file size can involve costs such as lower quality (lossy) or extra computation time for compress/decompress.

Data set

A collection of related data, often organized like a table with rows (records) and columns (variables).

Data vs information vs knowledge

Data = raw values; Information = processed/organized data with meaning; Knowledge = conclusions/decisions drawn from information.

Sampling bias

Bias caused when the people/items measured are not representative of the larger population, leading to misleading conclusions.

Data cleaning

Fixing or removing issues in data (duplicates, inconsistent formats, missing values, errors) to improve analysis accuracy.

Privacy concerns (data collection)

Risks that collected data (especially when combined across sources) can reveal sensitive information or be used in unexpected ways.

Correlation vs causation

Correlation means two variables move together; it does not prove that one causes the other (a third factor or coincidence may exist).

Data abstraction

Representing complex real-world information in a simplified form that is useful for computation (choosing relevant details).

List (AP CSP)

An ordered collection of items used to store and process data; supports operations like traversal, filtering, and aggregation.

1-based indexing

An indexing convention (used in AP CSP pseudocode) where the first element of a list is at index 1, not 0.

List traversal

An algorithmic process that visits each element in a list to compute results such as a count, sum, maximum, or filtered list.

Filtering

Keeping only the data items (rows/elements) that satisfy a condition, reducing the data to what’s relevant.

Parallel lists

A way to represent related attributes using multiple lists aligned by index (error-prone if the lists become misaligned).