📚 Knowledge Library — Topic 1 — Data Representation

Binary and Hexadecimal

Understand how computers represent numbers using simple patterns of 1s and 0s, and why hexadecimal makes long binary values easier to read.

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1. Invitation

You are not learning a new language.

You are learning how computers count. Binary and hexadecimal can look strange at first, but they follow a clear pattern.

Computers store every type of data using binary. Text, images, sound and video all become patterns of 1s and 0s.

💡 Remember: once you understand the pattern, the topic becomes much less scary.
Figure 1.1
Everything becomes Binary
TEXT
IMAGE
SOUND
↓
BINARY
2. The Big Idea

Computers only need two states.

A computer is built from tiny electronic circuits. These circuits can be in one of two states: off or on.

We represent these two states using the digits 0 and 1. This is why binary is called a base-2 number system.

💡 Binary uses only two digits: 0 and 1.
Figure 2.1
Electronic Switch
OFF ───► 0

ON ───► 1
3. Worked Example

Converting binary to denary.

Each binary column has a place value. Starting on the right, the values double each time.

To convert binary to denary, add the place values where there is a 1.

Convert 00101101₂ to denary

128
64
32
16
8
4
2
1
0
0
1
0
1
1
0
1
32 + 8 + 4 + 1 = 45
Figure 3.1
Binary Place Values
128 64 32 16
8 4 2 1
Each column is twice the value of the column to its right.
4. Hexadecimal Reference

Hexadecimal is a shortcut for binary.

Hexadecimal uses sixteen values. The digits 0 to 9 work as normal. The letters A to F represent the values 10 to 15.

One hexadecimal digit can represent exactly four binary bits.

🎯 Exam Tip: Learn A = 10, B = 11, C = 12, D = 13, E = 14 and F = 15.
Figure 4.1
Four Bits to One Hex Digit
1111₂
↓
F₁₆
1111₂ = 15₁₀ = F₁₆
DecimalBinaryHexadecimal
000000
100011
200102
300113
401004
501015
601106
701117
810008
910019
101010A
111011B
121100C
131101D
141110E
151111F
5. Common Mistake

1111₂ is not the same as 1111₁₀.

Students sometimes read binary as if it were a denary number. This causes major mistakes in conversions.

⚠️ Common Mistake: 1111₂ means 8 + 4 + 2 + 1, not one thousand one hundred and eleven.
Figure 5.1
Correct Interpretation
1111₂
= 8 + 4 + 2 + 1
= 15₁₀