The One Thing You Need to Know About this Big Idea:
This unit is all about how computers represent data, and how they can store and process ever-increasing quantities of it.
2.1 Binary Numbers
Learning Objective: Explain how data can be represented using bits.
Learning Objective: Explain the consequences of using bits to represent data.
**Learning Objective: For binary numbers, calculate the binary (base 2) equivalent of a positive integer (base 10) and vice versa; compare and order binary numbers. **
Key Ideas
- computers store data in bits
- computers use machine code, which operate on the binary system (digits are either 0 or 1)
- any decimal number can be expressed as a binary number and vice versa
- the same sequence of bits can represent different types of data depending on the context
- abstraction hides irrelevant details from users
- analog / digital representation of data
- overflow and rounding errors result from using bits to represent data
Vocabulary
- data
- bits
- number base
- machine code
- binary system
- byte
- hexadecimal
- abstraction
- analog data
- digital data
- sampling technique
- overflow error
- rounding error
Resources
2.2 Data Compression
Learning Objective: Compare data compression algorithms to determine which is best in a particular context.
Key Ideas
- data compression can reduce the number of bits when transmitting or storing data
- fewer bits doesn't necessarily mean less information
- lossless data compression is preferred if your main concern is the quality of your file or if you need to be able to reconstruct your original file
- lossy data compression is preferred if your main concern is minimizing how big your file is or how long it'll take to send or receive it
Vocabulary
- lossless compression algorithms
- lossy compression algorithms
Resources
2.3 Extracting Information from Data
Learning Objective: Describe what information can be extracted from data.
**Learning Objective: Describe what information can be extracted from metadata. **
Learning Objective: Identify the challenges associated with processing data.
Key Ideas
- by examining data closely, we can identify trends, make connections and address problems
- metadata allow data to be structured and organized
- changes and deletions to metadata don't change the primary data
- cleaning data is a process that makes the data uniform without changing their meaning
- problems of bias are often created by the type or source of data being collected; just collecting more data won't make this problem go away
Vocabulary
- information
- metadata
- cleaning data
Resources
🔗 2.3: Extracting Information from Data
2.4 Using Programs with Data
Learning Objective: Extract information from data using a program.
Learning Objective: Explain how programs can be used to gain insight and knowledge from data.
Key Ideas
- data processing programs can help you acquire information from data
- data filtering systems help with finding information and recognizing patterns
- manipulating data by combining, clustering or classifying it can bring out new information and patterns previously unseen in the raw data, making it a helpful tool for data analysis
Vocabulary
- data transformation
- data filtering
Resources
🔗 2.4: Using Programs with Data
Exam Weighing
- 17-22% of the AP Exam
- Practically, this translates to about 20 questions on the test.
Vocabulary
The following words are mentioned explicitly in the College Board Course and Exam Description for this topic.
| Term | Definition |
|---|---|
| abstraction | The process of reducing complexity by focusing on main ideas and hiding irrelevant details to allow focus on the essential concept. |
| analog data | Data that have values changing smoothly and continuously over time, such as pitch, volume, or position. |
| binary | A base-2 number system that uses only the digits 0 and 1 to represent data. |
| bit | Shorthand for binary digit; the smallest unit of data in computing, represented as either 0 or 1. |
| byte | A unit of digital data consisting of 8 bits. |
| constants | Fixed data values that do not change during program execution. |
| data | Information represented in a form that can be processed by a program, such as numbers, text, or records. |
| decimal | A base-10 number system that uses the digits 0-9 to represent data. |
| fixed number of bits | A predetermined, limited quantity of bits allocated to represent a data value in programming languages, which constrains the range of representable values. |
| integers | Whole numbers (positive, negative, or zero) that are represented in programming languages using a fixed number of bits. |
| number bases | Different systems for representing numerical values, such as binary (base 2) and decimal (base 10). |
| overflow | An error that occurs when a computed value exceeds the maximum value that can be represented by a fixed number of bits. |
| place value | The numeric value assigned to a digit's position in a number, determined by the base raised to the power of the position. |
| real numbers | Numbers that include both integers and decimal values, represented in programming languages with a fixed number of bits as approximations. |
| roundoff error | An error that occurs when real numbers are approximated in computer storage due to limitations in the fixed number of bits used to represent them. |
| sampling | A technique for approximating analog data digitally by measuring values of an analog signal at regular intervals. |
| variable | A named container in a program that stores a value which can be changed through assignment. |