Exploring AP CSP Big Ideas 2: Understanding Data
This big idea is about understanding how data can be represented, changed, and compressed. Here, we explain the main parts of this big Idea in short and easy sentences.
Concepts
There are several concepts to learn relating to big idea 2 about data transformation.
- binary numbers
- data compression
- information extraction
We can look at the key concepts in each of the big idea 2 sections, and within the big idea itself.
2.1 Binary Numbers
Learning Objectives
- Explain how data can be represented using bits
- Explain the binary number system, and how standard integers can be converted to binary numbers and binary numbers back to integers.
Data Representation
Bits
Bits are used to store data in computers. The computer takes input from devices like the mouse and keyboard and transforms it into machine code. This machine code is based on the binary numbers system where everything is represented using just 0 and 1 digits.
Bytes
The number of bits in a byte is 8.
The number of bits stored or transmitted at one time is normally in bytes.
Computers move data and instructions in pieces at a time, these pieces of data are based on 8 digits, 8 zeros and ones, called a byte. More than one byte can be used, so we often hear computers are 32-bit (four bytes) or 64-bit (eight bytes), because that is the size that the computer moves the data.
We can see how computers represent data in 0s and 1s by explaining binary, bits and bytes in
- numbers (integers)
- text
- images and video
- and sound
Integer Numbers to Binary
Integers are simple numbers like 1, 2, 10, 100 etc. These can be represented in the binary system used by computers.
To understand how the binary number system works, we need to know the meaning of a series of 0s and 1s. Each digit from the right represents a value of 2 to the power of 0, 1, 2, 3, etc. So, for example, if we have 5 digits, say 11111 then this represents 1, 2, 4, 8, and 16. 1111 represents 1, 2, 4, 8, and 111111 represents 1, 2, 4, 8, 16 and 32.
in the sequence of bits, or 0s and 1s, we can convert a number to binary by adding these values until we have the value of the integer. For each of the values 1,2,4, 8 etc if we wish to add the number we use a 1, and if we do not use it then we use a 0.
Let’s see some examples:
- 1 in binary is 1
- 2 in binary is 10
- 3 in binary is 11
- 4 in binary is 100
- 8 in binary is 1000
- 16 in binary is 10000
- 32 in binary is 100000
- 7 in binary is 111
- 15 in binary is 1111
- 31 in binary is 11111
- 9 in binary is 1001
- 17 in binary is 10001
- 33 in binary is 100001
Binary to Decimal
Binary numbers can be converted to decimal numbers. We calculate the values of the 1s in the binary number, add them, and have the integer number value of the binary number.
If you have an exam question and you want to make sure the answer is correct you can write the sequence of values for each digit, like this
- 8 4 2 1 for a 4-digit binary number like 1011
- 16 8 4 2 1 for a 5-digit binary number like 10110
- 32 16 8 4 2 1 for a 6-digit binary number like 101101
Lets covert the following binary numbers to integers:
- 1011 is 11
- 1011 is (1 x 8) + (0 x 4) + ( 1 x 2)+ ( 1 x 1), this is 8+2+1 = 11
- 10110 is 22
- 10110 is (1 x 16) + (0 x 8) + (1 x 4) + ( 1 x 2)+ ( 0 x 1), this is 16+4+2 = 22
- 101101 is 43
- 101011 is (1 x 32) + (0 x 16) +(1 x 8) + (0 x 4) + ( 1 x 2)+ ( 1 x 1), this is 32+8+2+1 = 43
2.2 Data Compression
- representation of data is analog is real life, digital by devices
- errors can occur using bits to represent data, such as overflow and rounding errors
original data is analog data and digital data
AP Computer Science Principles Exam Preparation
Everything you need to prepare for the ap csp exam, including dates, practice questions, previous results and a score calculator chart. Good luck!
2.3 Extracting Information from Data
2.4 Using Programs with Data
Vocabulary
- Abstraction hides irrelevant details from users
- Analog data: Continuous data, like sound or light, that changes smoothly.
- Analog signal: Continuous data represented by smooth changes in values, such as sound or light waves.
- Binary: A number system using only 0 and 1.
- Binary system: A method of representing data using only two states, 0 and 1.
- Bit: The smallest unit of data in computing, representing a 0 or 1.
- Bits: A plural form of bit, referring to multiple units of data.
- Byte: A group of 8 bits.
- Compression: Reducing the size of data for storage or transmission.
- Data: Information that can be processed or stored by a computer.
- Digital data: Data represented in binary format, consisting of discrete values (0s and 1s).
- Hexadecimal: A number system based on 16, using the digits 0–9 and the letters A–F.
- Lossless compression: A way to reduce file size without losing any data.
- Lossy compression: A way to reduce file size by removing some data.
- Machine code: The lowest-level programming language, understood directly by a computer’s processor.
- Metadata: Data that describes other data, such as file size or creation date.
- Number base: The number of unique digits used in a numbering system (e.g., base 2 for binary, base 10 for decimal).
- Overflow error: An error that occurs when a calculation exceeds the storage capacity of a system.
- Programming language: A way for programmers to write instructions for computers.
- Rounding error: An error caused by approximating a number during storage or calculations.
- Run-length encoding: A simple compression method that reduces repeated data.
- Sampling technique: A method of converting analog data to digital by taking measurements at regular intervals.
FAQ
These have been replaced by the 5 big ideas given above.
Useful Information
Data can be represented as binary sequences of 0s and 1s.
A fixed number of bits is used to store or transmit data. More bits allow a wider range of values to be represented.
When transforming data, the goal is often to reduce its size while keeping it meaningful. This is done using compression techniques.
Lossy compression reduces file size by removing some data, but this can cause approximate reconstruction of the original file.
Data mining is a process that analyzes large datasets to find useful patterns.