Data Representation Grade 10

Computers only understand two states: on (1) and off (0). Everything — text, images, sound, video — must first be converted to those 1s and 0s before a computer can process it. This page explains how that conversion works.

Why Only 1s and 0s?

Deep inside your computer, everything is built from tiny transistors — microscopic electronic switches. Each switch can only be in one of two states: on (1) or off (0). This is called binary because there are only two options.

A single 1 or 0 is called a bit (short for binary digit). On its own, one bit can only represent two things. But group 8 bits together into a byte, and suddenly you can represent 256 different values (2⁸ = 256) — enough for every letter, digit, and common symbol.

Bits and Bytes — Visual Diagram

Eight bits grouped together form one byte. The example below shows the byte 01000001 — the binary code for the letter A in ASCII.

Number Systems Overview

Binary (Base 2)

In decimal, each column is worth 10× the column to its right (1, 10, 100, 1000…). In binary, each column is worth 2× the column to its right — these are the powers of 2.

Step-by-Step Conversion Examples

Binary → Decimal

Multiply each bit by its place value, then add them all up. Only count the columns where the bit is 1.

(0 × 2⁷) + (0 × 2⁶) + (1 × 2⁵) + (0 × 2⁴) + (1 × 2³) + (1 × 2²) + (0 × 2¹) + (1 × 2⁰)

= (0 × 128) + (0 × 64) + (1 × 32) + (0 × 16) + (1 × 8) + (1 × 4) + (0 × 2) + (1 × 1)

= 0 + 0 + 32 + 0 + 8 + 4 + 0 + 1

= 45

(1 × 2⁴) + (0 × 2³) + (1 × 2²) + (1 × 2¹) + (0 × 2⁰)

= (1 × 16) + (0 × 8) + (1 × 4) + (1 × 2) + (0 × 1)

= 16 + 0 + 4 + 2 + 0

= 22

Decimal → Binary (Divide by 2 Method)

Divide the number by 2 repeatedly. Write down each remainder. Read the remainders from bottom to top.

25 ÷ 2 = 12  remainder  1   ← LSB (written last, read first from bottom)
12 ÷ 2 =  6  remainder  0
 6 ÷ 2 =  3  remainder  0
 3 ÷ 2 =  1  remainder  1
 1 ÷ 2 =  0  remainder  1   ← MSB (written first, read last from bottom)

Read remainders bottom to top:  1  1  0  0  1
                                                = 11001₂

Verify:  16 + 8 + 0 + 0 + 1 = 25 ✓

13 ÷ 2 = 6  remainder  1
 6 ÷ 2 = 3  remainder  0
 3 ÷ 2 = 1  remainder  1
 1 ÷ 2 = 0  remainder  1

Read bottom to top:  1  1  0  1  =  1101₂

Verify:  8 + 4 + 0 + 1 = 13 ✓

Hexadecimal (Base 16)

Hexadecimal (hex) uses 16 symbols: the digits 0–9, then the letters A–F for values 10–15. Because one hex digit represents exactly 4 binary bits, hex is a much shorter way to write binary numbers. For example, 11111111 in binary is just FF in hex.

Hex Digit Table

Hex → Decimal Conversion

Each position in hex is worth 16× the position to its right (just like binary uses powers of 2, hex uses powers of 16).

2A₁₆ has two digits: 2 and A (=10)

(2 × 16¹) + (A × 16⁰)

= (2 × 16) + (10 × 1)

= 32 + 10

= 42₁₀

3F₁₆ has two digits: 3 and F (=15)

(3 × 16¹) + (F × 16⁰)

= (3 × 16) + (15 × 1)

= 48 + 15

= 63₁₀

Decimal → Hex Conversion (Divide by 16)

200 ÷ 16 = 12  remainder  8    →  8
 12 ÷ 16 =  0  remainder  12   →  C  (12 in hex = C)

Read remainders bottom to top:  C  8  →  C8₁₆

Verify:  12 × 16 + 8 = 192 + 8 = 200 ✓

ASCII — Storing Text

A computer stores text by mapping each character to a number. The most common mapping is ASCII (American Standard Code for Information Interchange). Each character has a unique number — a code — which is then stored in binary.

Key ASCII Values to Memorise

Unicode and UTF-8

Data Representation in Delphi

// Ord: char → ASCII number
iCode := Ord('A');         // = 65
iCode := Ord('a');         // = 97

// Chr: ASCII number → char
cChar := Chr(65);           // = 'A'
cChar := Chr(97);           // = 'a'

// Convert lowercase to uppercase using the +32 rule:
cUpper := Chr(Ord(cLower) - 32);

// Print ASCII values of each character in a string
for i := 1 to Length(sText) do
  memOut.Lines.Add(sText[i] + ' = ' + IntToStr(Ord(sText[i])));

Storage Units

File Compression

Compression reduces the amount of disk space a file uses. Decompression restores a compressed file back to a usable form. Higher compression means a smaller file size and faster download/streaming, but too much compression can reduce quality (pixelation in images, distortion in audio).