Cambridge IGCSE Computer Science (0478) · Data representation
Mini-Lesson
Data representation
Computers store everything — numbers, text, images and sound — as binary: patterns of 0s and 1s. This mini-lesson covers number systems (binary, denary, hexadecimal) and conversions, binary arithmetic and logical shifts, two’s complement (Extended), how text, images and sound are represented, data storage units, and compression.
Work through each screen, answer the questions (some are conversions and calculations) and collect ⭐ stars. Watch for the Extended flag. Press Start when ready.
Number systems · binary & denary
Binary and denary
Denary (decimal) is base 10 — digits 0–9. Binary is base 2 — only 0 and 1. Each binary digit is a bit; 8 bits make a byte. In an 8-bit byte each column has a place value:
Add the place values wherever there is a 1: here 32 + 8 + 4 + 1 = 45.
Worked example — denary to binary (45)
Fit 45 into 128 64 32 16 8 4 2 1: 45 = 32 + 8 + 4 + 1.
So 45 = 0010 1101.
Tip: the largest number in 8 bits is 11111111 = 255 (that’s 256 different values, 0–255).
Convert
Your turn — binary to denary
1Convert the binary number 10011010 to denary.
Hint: 128 + 16 + 8 + 2.
Quick check
Denary to binary
?Which 8-bit binary number represents the denary value 100?
Number systems · hexadecimal
Hexadecimal
Hexadecimal is base 16, using digits 0–9 then A B C D E F for 10–15. It is a shorthand for binary: one hex digit = exactly 4 bits (a nibble), so a byte is just two hex digits.
11001000 splits into 1100 (C) and 1000 (8), so it is C8 in hex.
Worked example — hex C8 to denary
C = 12, so C8 = (12 × 16) + 8 = 192 + 8 = 200.
Uses: hex is used for MAC addresses, IP (IPv6) addresses, colour codes (e.g. #FF0000) and memory dumps — it is shorter and easier for humans than long binary strings.
Convert
Your turn — hex to denary
2Convert the hexadecimal number 2F to denary.
Hint: 2 = 2×16 = 32, and F = 15. Add them.
Quick check
Denary to hex
?What is the denary number 200 written in hexadecimal?
Binary arithmetic & logical shifts
Binary addition & logical shifts
Adding binary works like denary, but you carry when a column reaches 2 (10 in binary): 0+0=0, 0+1=1, 1+1=10 (write 0, carry 1), 1+1+1=11 (write 1, carry 1).
Worked example — 01001111 + 00101011
79 + 43 in denary. Adding the bits with carries gives 01111010 = 122. Check: 64+32+16+8+2 = 122.
A logical shift moves all the bits left or right, filling the empty end with 0. A left shift by 1 multiplies the number by 2; a right shift by 1 divides by 2 (whole-number part). Bits shifted out of the end are lost.
Overflow: if a sum needs more than 8 bits (over 255), the extra carry can’t be stored — this is an overflow error.
Calculate
Your turn — binary addition
3Add the binary numbers 00110101 + 00010110. Give the denary value of the answer.
Hint: 00110101 = 53 and 00010110 = 22. 53 + 22.
Quick check
Logical shift
?The 8-bit number 00010100 (denary 20) is given a logical shift right by 2 places. What is the new denary value?
Extended · two’s complement
Two’s complement (negative numbers)
To store negative whole numbers, computers use two’s complement. In 8-bit two’s complement the left-most bit is negative: its place value is −128, and the rest stay 64, 32 … 1.
Worked example — write −5 in 8-bit two’s complement
1. Write +5 = 00000101.
2. Invert every bit (flip 0↔1) → 11111010.
3. Add 1 → 11111011.
Check: −128 + 64 + 32 + 16 + 8 + 2 + 1 = −5. ✓
Spot a negative: if the left-most bit is 1, the number is negative. Range in 8 bits is −128 to +127.
Extended · Calculate
Your turn — two’s complement
4The 8-bit two’s complement number 11110000 represents which denary value? (Remember the left bit is −128.)
Hint: −128 + 64 + 32 + 16 = ? (the last four bits are 0).
Representing text, sound & images
Text, sound & images
Text — each character has a binary code in a character set. ASCII uses 7 (or 8) bits; Unicode uses more bits so it can represent many more characters, including other alphabets and emoji.
Images (bitmaps) — made of pixels. Colour depth = number of bits per pixel (more bits → more colours). Resolution = number of pixels (width × height). File size (bits) = width × height × colour depth.
Sound — the analogue wave is sampled at regular intervals. Sample rate = samples per second (Hz); sample resolution = bits per sample. Higher values → more accurate sound but larger files.
Sampling turns a smooth wave into numbers the computer can store.Calculate
Your turn — image file size
?A bitmap image is 10 pixels wide and 8 pixels tall, with a colour depth of 4 bits. What is its file size in bits?
Data storage & units
Measuring data storage
The smallest unit is the bit; 8 bits = 1 byte. Larger units go up in 1024s (210):
1 kibibyte (KiB) = 1024 bytes
1 mebibyte (MiB) = 1024 KiB
1 gibibyte (GiB) = 1024 MiB
1 tebibyte (TiB) = 1024 GiB
Note: in everyday adverts kilo/mega often mean 1000, but Cambridge 0478 uses the IEC units (kibi, mebi, gibi…) which are powers of 1024.
Match it
Match the term to its meaning
Tap a description on the left, then its matching term on the right.
Description
Term
Compression
Compression
Compression reduces a file’s size so it needs less storage and transmits faster. There are two types:
Lossless — no data is lost; the original file can be perfectly rebuilt. Uses techniques like run-length encoding (RLE). Used for text and program files.
Lossy — some data is permanently removed (e.g. detail the eye/ear barely notices). Gives much smaller files but lower quality. Used for photos (JPEG) and music (MP3).
Key difference: lossless can be fully reversed; lossy cannot — the removed data is gone for good.
Quick check
Which compression?
?A programmer must compress a text file so it can be perfectly restored later with no characters lost. Which type of compression should they use?