Binary, Denary & Hexadecimal Conversion

• Computing
• Lower Secondary (Key Stage 3)

Binary, Denary & Hexadecimal Conversion

1. What base is the binary system
2. What base is the denary system?
3. How is 11 represented in binary?

Binary → Denary

Example: Convert 1010 to denary

1           0             1                0

1. Write the 8-4-2-1 columns
2. Place each binary digit underneath
3. Add the columns where the digit is 1

1×8 = 8

1×2 = 2

Total = (8+2) = 10

Convert 0101 to Denary

0          1          0           1

Denary → Binary

Example: convert 13 to binary

1. Start with the largest column that fits into your number.

13 fits into 8 → write 1

13 − 8 = 5

1

Denary → Binary

Example: convert 13 to binary

2. Move to the next column (4).

5 fits into 4 → write 1

5 − 4 = 1

1

1

Denary → Binary

Example: convert 13 to binary

3. Next column (2).

1 does NOT fit into 2 → write 0

1

1

0

Denary → Binary

Example: convert 13 to binary

4. Final column (1).

1 fits into 1 → write 1

➡ Result: 1101

1

1

0

1

Convert 15 to binary

What is the biggest number you can show using 4 binary bits?

1. 15
2. 8
3. 4
4. 16

• In denary (base 10), each column is a power of 10 (1, 10, 100, 1000…), so each place is ten times bigger than the one before.

• In binary (base 2), each column doubles (1, 2, 4, 8, 16…), because only the digits 0 and 1 can be used.

• In hexadecimal (base 16), each column is a power of 16 (1, 16, 256, 4096…), allowing a single digit to represent much larger values.

Match the binary to the hex

0

A

F

C

6

0000

1010

1111

1100

01100

Binary → Hex

1011

1110

Hex → Binary

A

F

3

1. Binary → Hex

i). 1011

ii). 1110

2.Hex → Binary

i).A

ii).F

iii).3

Extension

Extension