Fundamentals of data representation

What is binary in computing?

System using just 0s and 1s to represent data and instructions

What is a bit?

The smallest unit of data, value of 0 or 1

Why do computers use binary?

Electronic circuits can easily represent two states (on/off)

How are numbers represented in binary?

As sequences of bits (e.g., 10101010)

What range of decimal values can 8 bits represent?

0 to 255

How do you convert decimal 25 to binary?

00011001

How do you convert binary 10110011 to decimal?

179

What is a byte?

8 bits grouped together

What is a kilobyte (kB)?

1000 bytes

What is a megabyte (MB)?

1,000,000 bytes

What is a gigabyte (GB)?

1,000,000,000 bytes

What is a terabyte (TB)?

1,000,000,000,000 bytes

What is hexadecimal?

Number system with base 16, digits 0-9, letters A-F

Why is hexadecimal used in computer science?

Shortens long binary numbers, easier for humans to read

How do you convert decimal 255 to hexadecimal?

FF

How do you convert hexadecimal 3A to decimal?

58

How are numbers converted from binary to hexadecimal?

Group binary digits in 4s, convert each to hex

How do you convert hexadecimal 4F to binary?

01001111

How do you convert binary 11011101 to hexadecimal?

DD

How can hexadecimal represent colours?

Each pair for R, G, B channels (e.g., #FF0044)

How are bytes described using prefixes?

kilo, mega, giga, tera to compare file sizes

What is a character set?

Table mapping characters (letters, digits, symbols) to binary codes

What is ASCII?

Standard character set, uses 7 or 8 bits for each character

What code does capital 'A' have in ASCII?

65

How are ASCII codes sequenced?

Grouped; A = 65, B = 66, etc.

What is Unicode?

Universal character set supporting worldwide languages and symbols

What is an advantage of Unicode over ASCII?

Represents many more characters, useful for global data

Up to what code are Unicode and ASCII the same?

127 (first 128 characters)

What is a pixel?

Single point of colour in a digital image

What is a bitmap image?

Image stored as a grid of pixels, with each pixel's colour in binary

How do you calculate bitmap file size (bits)?

Width × Height × Colour depth

How do you calculate image size in bytes?

Width × Height × Colour depth ÷ 8

If image is 200x100 pixels at 8-bit colour depth, size in bytes?

200 × 100 × 8 ÷ 8 = 20,000 bytes

What is colour depth?

Number of bits per pixel to represent colours

What happens when you increase colour depth?

More colours per pixel, larger file size

What happens when you increase image resolution?

More pixels, higher quality, bigger file size

How is each pixel in a bitmap stored?

As a binary value representing its colour

How do you convert binary data into an image?

Translate the binary values for each pixel into the corresponding image display

How do you convert an image into binary data?

Write the bit pattern for each pixel’s colour

What is sound in computing?

Analogue signal that must be sampled/digitised for computers

What is sample rate?

Number of samples per second, measured in hertz (Hz)

What is sample resolution?

Number of bits per sample

How do you calculate sound file size (bits)?

Sample rate × Sample resolution × Seconds

If sampling at 44,100Hz, 16 bits/sample, for 10 seconds, file size?

44,100 × 16 × 10 = 7,056,000 bits

What is analogue to digital conversion?

Sampling a sound’s amplitude at intervals, encoding each value in binary

What does higher sample rate mean?

Better audio quality, bigger file size

What does higher sample resolution mean?

Better accuracy, more storage space needed

Why is data compressed?

To save space, reduce transfer time and costs, easier storage

What is data compression?

Reducing number of bits needed to store data

What is lossless compression?

Method that reduces file size without losing any information

What is lossy compression?

Method that discards some data for higher savings, less quality

What is Huffman coding?

Compression using variable length codes for common data, based on a tree

How is a Huffman tree used?

Assign shorter codes to frequent items, longer codes to rare items

How do you calculate the number of bits saved by Huffman coding?

Compare original code length to Huffman code length

What is run length encoding (RLE)?

Compresses data by storing pairs of frequency and value for repeated items

Give an RLE example for 0000011100000011.

5 0 3 1 6 0 2 1

How does RLE save space?

Encodes runs of repeated values more efficiently

How do you encode a bitmap row with RLE?

List frequency/value pairs for each stretch of similar pixels

What type of data is suitable for RLE?

Data with lots of repeated values (e.g. simple bitmaps)

How many bits does ASCII character set use?

7 or 8 bits per character

Give a reason to compress files before sending over the Internet.

Faster transfer, less bandwidth used

What is the difference between ASCII and extended ASCII?

Extended has more characters (up to 255)

What is the purpose of applying binary shift?

Multiply or divide a binary number by powers of 2

What does a left binary shift do?

Multiplies by 2 for each place shifted

What does a right binary shift do?

Divides by 2 for each place shifted

When would you use binary shifts?

In simple binary arithmetic, graphics, data manipulation

How many values can 3 bits represent?

8 (2^3)

How is text represented in binary?

As a pattern according to its character set (e.g. ASCII)

How are images displayed in computers?

Each pixel’s binary value shown in its location on screen

How is sound represented as binary?

Each sample’s amplitude value stored as a binary number

What is the effect of high sample rate and resolution on music files?

Larger size, better quality

What is a nibble?

4 bits, half a byte

Can binary be used to represent integers, text, images, sounds?

Yes, all types by encoding each accordingly

What is a frequency/data pair in RLE?

Number of times a value appears, and the actual value itself

What coding system supports worldwide alphabets?

Unicode

What is a significant advantage of compressing data in storage and transmission?

Saves disk space and network bandwidth

How do you use a character encoding table?

Find binary/hex value for each symbol using table

Why do images with higher pixel count require more storage?

More data points (pixels) to encode

What is the difference between lossy and lossless compression?

Lossy removes data, lossless re-encodes without loss

Why is text best compressed using lossless methods?

You don't want to lose accuracy or data

How can ASCII be used to store numbers?

Encode digits as character codes ('1' = 49, etc)

How do you calculate file size for a sound file in bytes?

Multiply bits then divide by 8

How are hexadecimal codes sometimes shown?

With a prefix (e.g. 0x, #) or uppercase letters

Why are decimal prefixes (kilo, mega) used for bytes?

To simply compare/communicate file sizes

Why must analogue signals be converted for computers?

Computers process only digital (binary) data

How do you decode a Huffman coded message?

Follow the tree as per bits to each character

What is a pixel’s binary colour called?

Bit depth value

How does Unicode help with global communication?

Covers characters for most languages worldwide

How does increasing width and height of a bitmap affect file size?

Size increases proportionally with more pixels

If a bitmap is 4x4 pixels, 8 bits per pixel, file size in bits?

4 × 4 × 8 = 128 bits

How do compression methods affect quality?

Lossless keeps perfect copy, lossy reduces quality

How does sample rate affect sound file size?

Higher sample rate = bigger file

How is binary addition performed?

Add columns, carry if more than 1; max three 1s in column for GCSE

What is logical binary shift?

Binary digits move left/right filling gaps with zeros

How does bitmap conversion to binary work?

Pixel colours converted to corresponding binary codes and vice versa