Start with the recap, study the fully worked examples, then use the practice problems to
check your understanding of Data Representation.
This page combines explanation, solved examples, and follow-up practice so you can move
from recognition to confident problem-solving in CS Thinking.
Concept Recap
The way information—numbers, text, images, and sound—is encoded as binary digits (0s and 1s) inside a computer. Different encoding schemes map real-world data to binary patterns, such as ASCII/Unicode for text, RGB for colors, and sampling for audio.
Turning real-world things (text, images, sound) into numbers a computer can process.
Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea:All data in computers is ultimately numbers—representation is the mapping.
Common stuck point:Different representations have trade-offs (quality vs. size).
Sense of Study hint:When learning about data representation, start with the simplest case: how integers map to binary. Then explore how text uses encoding tables (ASCII maps 'A' to 65). Finally, see how complex data like images and sound are broken into numbers that can be stored as binary.
Common Mistakes to Watch For
Before you work through the examples, skim the mistake guide so you know which shortcuts and
sign errors to avoid.
A computer stores the character 'A' as the number 65 (ASCII). Explain why computers use numbers to represent characters.
Answer
Computers only store binary numbers. Characters are represented by assigning each a unique number via an encoding scheme like ASCII.
First step
1
Step 1: Computers can only store binary numbers (sequences of 0s and 1s).
Full solution
2
Step 2: To store text, each character is assigned a unique number using an encoding scheme like ASCII (A=65, B=66, etc.).
3
Step 3: The binary for 65 is 01000001, which is what the computer actually stores. The encoding scheme maps between human-readable characters and binary.
Character encoding is a fundamental concept in data representation. ASCII uses 7 bits (128 characters), while Unicode extends this to represent characters from all writing systems worldwide.
Example 2
medium
Explain how a computer represents a colour image using binary. What are pixels and colour depth?
Example 3
easy
A pixel uses 1 byte for grayscale brightness (0=black, 255=white). How many distinct shades are possible?
Example 4
medium
The word 'CAT' is stored in ASCII with C=67, A=65, T=84. How many bytes does it take using 1 byte per character?
Example 5
medium
A grayscale image is 640×480 with 8 bits per pixel. What is its uncompressed size in kilobytes (use 1 KB =1000 bytes)?
Example 6
hard
You want to encode the 26 uppercase English letters using a fixed-length binary code. What is the minimum number of bits per letter, and how many unused codes remain?
Example 7
challenge
An 8-bit unsigned register holds 250 and is incremented by 10. What value does the register show, and what is the phenomenon called?
Practice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
medium
Sound is analogue but computers are digital. Describe how analogue sound is converted to digital form, using the terms 'sample rate' and 'bit depth'.
Example 2
hard
Explain the difference between lossless and lossy compression. Give an example of each and explain when you would choose one over the other.
Example 3
easy
Convert the binary number 10112 to decimal.Read off the decimal value from the highlighted place values
Example 4
easy
Convert decimal 5 to binary.Which place values are active in 5 = 101₂?
Example 5
easy
How many distinct values can 8 bits represent?
Example 6
easy
What is 255 in binary (8 bits)?All 8 bits set: the maximum unsigned 8-bit value
Example 7
easy
A color uses one byte each for R, G, B. How many bits total?
Example 8
easy
In ASCII, the letter 'A' is 65. What decimal code is 'B'?
Example 9
easy
True or false: the same image can be stored as PNG or JPEG with different trade-offs.
Example 10
easy
Doubling the bits per audio sample tends to do what to file size?
Example 11
medium
Convert 11012 to decimal, then add 3.
Example 12
medium
Convert decimal 26 to binary.26 = 16 + 8 + 2, so bits at those place values are 1
Example 13
medium
How many bits are needed to represent at least 1000 distinct values?
Example 14
medium
The word 'Hi' is stored in ASCII ('H'=72, 'i'=105). How many bytes does it take (1 byte/char)?
Example 15
medium
UTF-16 uses 2 bytes per character; ASCII uses 1. Storing 100 ASCII letters in each, how many more bytes does UTF-16 use?
Example 16
medium
A grayscale image is 4×4 pixels, 1 byte per pixel. How many bits to store it?
Example 17
medium
Add the binary numbers 1012+0112. Give the binary result.Binary addition: what is the result of 101₂ + 011₂?
Example 18
medium
Convert the binary 100102 to decimal.Sum only the place values where the bit is 1
Example 19
medium
A file uses 2 bytes per character. How many bits does a 10-character string take?
Example 20
challenge
An 8-bit unsigned counter holds 255 and is incremented by 1. What value results, and what is this phenomenon called?8-bit register at maximum value 255 — what happens when we add 1 more?
Example 21
challenge
Why can the decimal fraction 0.1 not be stored exactly in binary floating point? Give the core reason.
Example 22
challenge
Design a fixed-length encoding for the 4 directions N, E, S, W. What is the minimum bits per symbol, and give one valid assignment?
Example 23
easy
Convert the binary number 1102 to decimal.Which place values are active? Sum them to find the decimal equivalent
Example 24
easy
Convert decimal 9 to binary.9 = 8 + 1, so only the 8 and 1 place-value bits are set
Example 25
easy
How many bytes are in 16 bits?
Example 26
medium
Convert 101012 to decimal.Sum only the place values where the bit is 1 to find the decimal
Example 27
medium
Convert decimal 42 to binary.42 = 32 + 8 + 2, so bits at those place values are 1
Example 28
medium
How many bits are needed to represent at least 50 distinct values?
Example 29
medium
An image is 100×100 pixels with 24-bit color. What is its uncompressed size in bytes?
A song is 3 minutes long, sampled at 44100 Hz, stereo (2 channels), 16 bits/sample. What is the uncompressed file size in megabytes (use 1 MB =106 bytes)?
Example 34
hard
Convert decimal 200 to binary (8 bits).
Example 35
hard
Two characters in ASCII are stored as 0100100001101001. What word is this?Two bytes stored in memory — map each decimal value to its ASCII character
Example 36
hard
A PNG of a photo is 2.5 MB; the same photo saved as JPEG is 0.4 MB but slightly blurry. What kind of compression is each, and why is JPEG smaller?
Example 37
challenge
A signed 8-bit two's complement byte stores −1. Give the bit pattern.
Example 38
challenge
You design a 3-bit code for 8 symbols, but later need a 9th symbol. What is the minimum number of bits needed now, and what is the cost in storage for 1000 symbols?