Welcome to Digital Data!
Welcome to your study notes for the Digital Data unit of CCEA GCSE Digital Technology! Have you ever wondered how a smartphone stores thousands of photos, plays your favourite songs, or sends text messages in a fraction of a second? At the most basic level, computers do all of this using nothing more than simple electrical switches turned on or off.
Don't worry if computer numbers and conversions seem tricky at first. We are going to break everything down step-by-step with simple rules, practical examples, and memory tricks to help you score top marks in your exam!
1. Data vs. Information
People often mix up the words data and information, but in Digital Technology, they have very specific meanings.
What is Data?
Data consists of raw, unorganised facts, figures, numbers, or symbols that have no meaning on their own.
Example: The number \(14052008\) on a piece of paper is just raw data. You do not know if it is a phone number, a bank balance, a barcode, or a date.
What is Information?
Information is data that has been processed, structured, or given a context so that it becomes meaningful and useful.
Example: If we add formatting to that number to show \(14/05/2008\) and label it as a "Date of Birth", it becomes information.
The Golden Rule:
\(Data + Processing / Context = Information\)
Key Takeaway:
Data is raw facts without meaning. When data is processed or given context, it becomes information.
2. Units of Digital Storage
Inside a computer, everything is stored using electrical switches. A switch can only be in one of two states: OFF (represented by the number \(0\)) or ON (represented by the number \(1\)). This system of using only \(0\)s and \(1\)s is called the binary number system.
Storage Hierarchy (From Smallest to Largest)
• Bit (b): The smallest unit of data. A single binary digit: either a \(0\) or a \(1\).
• Nibble: A group of \(4\text{ bits}\) (e.g., \(1011\)).
• Byte (B): A group of \(8\text{ bits}\) (e.g., \(10110010\)). A single byte can store one character of text, like the letter 'A'.
• Kilobyte (KB): \(1024\text{ bytes}\) (or roughly \(1000\text{ bytes}\) in standard decimal usage).
• Megabyte (MB): \(1024\text{ KB}\) (used for MP3 songs, high-res photos).
• Gigabyte (GB): \(1024\text{ MB}\) (used for HD movies, video games).
• Terabyte (TB): \(1024\text{ GB}\) (used for large computer hard drives).
• Petabyte (PB): \(1024\text{ TB}\) (used by massive cloud data centres).
Memory Trick to remember the order:
Big Ninjas Bite Kittens, Make Giants Tremble Politely
(Bit, Nibble, Byte, Kilobyte, Megabyte, Gigabyte, Terabyte, Petabyte)
Common Mistake to Avoid: Watch your capital letters! A small \(b\) stands for bit, while a capital \(B\) stands for byte. There are \(8\text{ bits}\) in \(1\text{ byte}\).
Key Takeaway:
Computers store data in binary. \(8\text{ bits} = 1\text{ byte}\), and each larger unit increases by a factor of \(1024\) (or \(1000\)).
3. Binary Number System (Base-2)
Humans use the denary (or decimal) system, which is base-\(10\) and uses digits \(0\) to \(9\). Computers use the binary system, which is base-\(2\) and uses only \(0\) and \(1\).
8-Bit Binary Place Values
In denary, place values go up in tens (\(1, 10, 100, 1000\)). In binary, place values double as you move from right to left:
\(128\) | \(64\) | \(32\) | \(16\) | \(8\) | \(4\) | \(2\) | \(1\)
Converting 8-Bit Binary to Denary
Step-by-step method:
1. Write down the place value table (\(128, 64, 32, 16, 8, 4, 2, 1\)).
2. Place your binary number underneath the columns.
3. Add up all the column values where there is a \(1\).
Example: Convert binary \(10010110\) to denary.
• \(128 \times 1 = 128\)
• \(64 \times 0 = 0\)
• \(32 \times 0 = 0\)
• \(16 \times 1 = 16\)
• \(8 \times 0 = 0\)
• \(4 \times 1 = 4\)
• \(2 \times 1 = 2\)
• \(1 \times 0 = 0\)
Total: \(128 + 16 + 4 + 2 = 150\).
So, \(10010110\) in binary equals \(150\) in denary.
Converting Denary to 8-Bit Binary
Step-by-step method:
1. Write down the place value table: \(128, 64, 32, 16, 8, 4, 2, 1\).
2. Starting from the left (\(128\)), compare your number to the column value.
3. If your number is equal to or bigger than the place value, write a \(1\) and subtract that place value from your number.
4. If your number is smaller, write a \(0\) and move to the next column.
Example: Convert denary \(77\) to binary.
• Does \(128\) fit into \(77\)? No \(\rightarrow 0\)
• Does \(64\) fit into \(77\)? Yes \(\rightarrow 1\) (Remainder: \(77 - 64 = 13\))
• Does \(32\) fit into \(13\)? No \(\rightarrow 0\)
• Does \(16\) fit into \(13\)? No \(\rightarrow 0\)
• Does \(8\) fit into \(13\)? Yes \(\rightarrow 1\) (Remainder: \(13 - 8 = 5\))
• Does \(4\) fit into \(5\)? Yes \(\rightarrow 1\) (Remainder: \(5 - 4 = 1\))
• Does \(2\) fit into \(1\)? No \(\rightarrow 0\)
• Does \(1\) fit into \(1\)? Yes \(\rightarrow 1\) (Remainder: \(1 - 1 = 0\))
Answer: \(77\) in denary is \(01001101\) in binary.
Key Takeaway:
Always draw your \(8\)-bit grid (\(128, 64, 32, 16, 8, 4, 2, 1\)) on rough paper first. It makes binary conversions simple and error-free!
4. Binary Addition and Overflow Errors
Adding binary numbers is similar to adding regular numbers, but you carry over when you reach \(2\) instead of \(10\).
The 4 Golden Rules of Binary Addition:
• Rule 1: \(0 + 0 = 0\)
• Rule 2: \(0 + 1 = 1\)
• Rule 3: \(1 + 1 = 0\text{ carry }1\) (which represents \(2\) in binary: \(10\))
• Rule 4: \(1 + 1 + 1 = 1\text{ carry }1\) (which represents \(3\) in binary: \(11\))
Addition Example:
Add \(0101\) (\(5\)) and \(0011\) (\(3\)):
Line up the columns from right to left:
• Rightmost column: \(1 + 1 = 0\) (carry \(1\))
• Next column: \(0 + 1 + 1\text{ (carried)} = 0\) (carry \(1\))
• Next column: \(1 + 0 + 1\text{ (carried)} = 0\) (carry \(1\))
• Leftmost column: \(0 + 0 + 1\text{ (carried)} = 1\)
Result: \(1000\) (which equals \(8\) in denary: \(5 + 3 = 8\)).
What is an Overflow Error?
An overflow error occurs when the result of a binary calculation requires more bits than the computer has allocated to store it.
Example: If an \(8\)-bit register adds two numbers and the answer produces a \(9\)-bit result (greater than \(255\)), the extra \(9\text{th}\) bit on the far left is lost. This causes incorrect calculations and program crashes.
Key Takeaway:
Follow the four addition rules carefully from right to left. If an \(8\)-bit sum results in a \(9\text{th}\) bit, an overflow error has occurred.
5. Hexadecimal (Base-16)
Hexadecimal (often called Hex) is a base-\(16\) numbering system. It uses sixteen symbols: the numbers \(0\) to \(9\) followed by the letters \(A\) to \(F\).
Hexadecimal Values:
• \(0\) to \(9\) have their standard values (\(0\)–\(9\))
• \(A = 10\)
• \(B = 11\)
• \(C = 12\)
• \(D = 13\)
• \(E = 14\)
• \(F = 15\)
Why Do We Use Hexadecimal?
Computers do not process hexadecimal directly—they only understand binary. Hex is used strictly for human convenience because:
1. Hex is much shorter and more compact than binary strings.
2. Hex is easier for humans to read, write, and remember.
3. Humans make fewer mistakes when copying Hex compared to long strings of \(0\)s and \(1\)s.
4. It is extremely easy to convert between binary and Hex (each Hex character represents exactly \(1\text{ nibble}\) or \(4\text{ bits}\)).
Common Uses of Hexadecimal:
• HTML / CSS Colour Codes: e.g., \(\#FF0000\) is pure red, \(\#FFFFFF\) is white.
• MAC Addresses: Unique hardware network identifiers (e.g., \(00\text{:}1A\text{:}C2\text{:}7B\text{:}00\text{:}47\)).
• Error codes and memory dump displays during debugging.
Converting 8-Bit Binary to Hexadecimal
Step-by-step method:
1. Split the \(8\)-bit binary number into two \(4\)-bit nibbles.
2. Convert each nibble into denary using the place values (\(8, 4, 2, 1\)).
3. Convert any denary value from \(10\) to \(15\) into its corresponding letter (\(A\)–\(F\)).
4. Combine the two characters.
Example: Convert \(11011010\) to Hex.
• Split into two nibbles: \(1101\) and \(1010\).
• Left nibble (\(1101\)): \(8 + 4 + 0 + 1 = 13 \rightarrow \text{Letter } D\).
• Right nibble (\(1010\)): \(8 + 0 + 2 + 0 = 10 \rightarrow \text{Letter } A\).
• Combine: The Hex value is \(DA\).
Key Takeaway:
One Hex digit equals \(4\text{ bits}\) (a nibble). An \(8\)-bit byte is represented by exactly two Hex characters.
6. Representing Text (Character Sets)
To store text, computers assign a unique binary number to every single character (letters, numbers, punctuation marks, symbols, and special keys like space and enter). A collection of these character codes is called a character set.
1. ASCII (American Standard Code for Information Interchange)
• Standard ASCII: Uses \(7\text{ bits}\) per character, allowing it to represent \(2^7 = 128\) unique characters. This covers the English alphabet (upper and lower case), numbers \(0\)–\(9\), and common punctuation.
• Extended ASCII: Uses \(8\text{ bits}\) (\(1\text{ byte}\)) per character, representing \(2^8 = 256\) characters. This adds European accent marks and basic graphical symbols.
2. Unicode
• ASCII was limited to the English language. Unicode was created to support every written language in the world (including Chinese, Arabic, Japanese, and mathematical symbols) as well as emojis.
• Uses \(16\text{ bits}\) (\(65,536\) characters) or \(32\text{ bits}\) (over \(4\text{ billion}\) characters).
• Trade-off: Unicode can represent vastly more characters than ASCII, but it takes up more storage space per character.
Key Takeaway:
ASCII uses \(7\) or \(8\text{ bits}\) (limited mainly to English characters). Unicode uses \(16\) or \(32\text{ bits}\) to represent characters and emojis from all languages worldwide.
7. Representing Images
Digital images can be stored either as bitmaps or as vectors. The CCEA syllabus focuses primarily on bitmap images.
What is a Bitmap Image?
A bitmap image is made up of a grid of tiny individual squares of colour called pixels (picture elements). Each pixel is assigned a binary code representing its colour.
Key Terms for Bitmap Images:
• Resolution: The dimensions of the image, measured as the number of pixels wide by the number of pixels high (e.g., \(1920 \times 1080\)). A higher resolution means a clearer, sharper image with more detail, but a larger file size.
• Colour Depth (Bit Depth): The number of bits used to represent the colour of each individual pixel.
- \(1\text{-bit colour depth} = 2^1 = 2\text{ colours}\) (Monochrome: Black and White)
- \(2\text{-bit colour depth} = 2^2 = 4\text{ colours}\)
- \(8\text{-bit colour depth} = 2^8 = 256\text{ colours}\)
- \(24\text{-bit colour depth (True Colour)} = 2^{24} = 16.7\text{ million colours}\)
• Metadata: Extra data stored inside the image file that describes the file itself. Metadata includes: image dimensions, colour depth, file format, date created, GPS location, and camera settings.
Calculating Bitmap File Size:
\(\text{File Size (in bits)} = \text{Width (pixels)} \times \text{Height (pixels)} \times \text{Colour Depth (bits)}\)
Example: An image is \(100\text{ pixels}\) wide, \(50\text{ pixels}\) high, and has a colour depth of \(8\text{ bits}\).
\(\text{File Size} = 100 \times 50 \times 8 = 40,000\text{ bits}\).
To convert to bytes: \(40,000 \div 8 = 5,000\text{ bytes}\).
Key Takeaway:
Increasing resolution or colour depth increases the quality of the image, but also increases the required storage space.
8. Representing Sound
Sound waves in the real world are continuous and analogue. Computers can only store digital binary data, so sound must be converted from analogue to digital using an ADC (Analogue-to-Digital Converter) through a process called sampling.
How Sound is Sampled:
The amplitude (height/volume) of the sound wave is measured at regular intervals and recorded as a binary number.
Key Factors Affecting Sound Quality and File Size:
• Sample Rate: The number of samples taken per second, measured in Hertz (Hz) or Kilohertz (kHz). For example, CD quality audio uses a sample rate of \(44.1\text{ kHz}\) (\(44,100\text{ samples per second}\)).
• Sample Resolution (Bit Depth): The number of bits used to store each sample measurement. A higher bit depth allows a more accurate recording of dynamic range and volume variations.
• Duration: The length of the sound track in seconds.
Calculating Sound File Size:
\(\text{File Size (in bits)} = \text{Sample Rate (Hz)} \times \text{Sample Resolution (bits)} \times \text{Duration (seconds)}\)
Impact on Quality and Storage:
• Higher Sample Rate + Higher Bit Depth = Better sound quality (closer to original), but larger file size.
• Lower Sample Rate + Lower Bit Depth = Poorer sound quality, but smaller file size.
Key Takeaway:
Sound is digitised by taking samples at regular intervals. Higher sample rates and bit depths give better audio quality at the expense of larger file sizes.
9. Data Compression
Compression is the process of reducing the size of a file so that it takes up less storage space and can be transmitted faster over networks or the Internet.
1. Lossy Compression
• How it works: Permanently removes non-essential or less noticeable data from the file (e.g., sounds humans cannot hear, or very subtle colour differences).
• Advantages: Drastically reduces file size; fast download/upload times.
• Disadvantages: Permanent loss of original quality; the file cannot be restored to its original state.
• Common File Types: JPEG (images), MP3 (audio), MP4 (video).
2. Lossless Compression
• How it works: Compresses the data by finding repeated patterns and encoding them efficiently without throwing away any data at all.
• Advantages: No loss of quality; the original file can be reconstructed perfectly when decompressed.
• Disadvantages: Does not reduce file size as significantly as lossy compression.
• Essential for: Text documents, program code, spreadsheets, and medical scans (where losing even one character or pixel would be catastrophic).
• Common File Types: PNG (images), FLAC (audio), ZIP (archive files), PDF (documents).
Key Takeaway:
Lossy deletes data permanently to get the smallest possible file (ideal for media streaming). Lossless reduces file size without losing any data (essential for text, code, and files where exact accuracy is required).
Quick Summary Checklist for Revision
Before sitting your exam, make sure you can:
• Explain the difference between data and information.
• List storage units in order from bit up to petabyte.
• Convert between \(8\)-bit binary and denary.
• Add two \(8\)-bit binary numbers and identify an overflow error.
• Convert between binary and hexadecimal, and explain why Hex is used.
• Contrast ASCII and Unicode.
• Calculate the file sizes of bitmap images and digital audio recordings.
• Compare the advantages and disadvantages of lossy and lossless compression.