01 Key Concepts
Decimal (Base-10)
The system we use daily. Uses digits 0-9. Each place value is a power of 10.
Binary (Base-2)
Uses only digits 0 and 1. Each place value is a power of 2. Used inside computers.
Octal (Base-8)
Uses digits 0-7. Each place value is a power of 8.
Hexadecimal (Base-16)
Uses digits 0-9 and letters A-F (A=10 ... F=15). Each place value is a power of 16.
Converting Between Systems
To convert any base to decimal, multiply each digit by its place value (power of the base) and add the results.
03 Key Formulas
- Decimal value = sum of (digit x base^position), counting positions from 0 on the right.
04 Solved Examples
Example 1 Convert binary 1011 to decimal.
- Positions from right: 1(2^0), 1(2^1), 0(2^2), 1(2^3).
- = 1x8 + 0x4 + 1x2 + 1x1
- = 8 + 0 + 2 + 1
Answer: 11
Example 2 Convert decimal 25 to binary.
- Divide by 2 repeatedly, recording remainders: 25÷2=12 r1, 12÷2=6 r0, 6÷2=3 r0, 3÷2=1 r1, 1÷2=0 r1.
- Read remainders bottom to top: 1 1 0 0 1
Answer: 11001
Example 3 Convert hexadecimal 2F to decimal.
- 2F means 2 in the 16s place and F (=15) in the 1s place.
- = 2x16 + 15x1
- = 32 + 15
Answer: 47
05 Practice Questions
1Convert binary 101 to decimal.
5
2Convert decimal 10 to binary.
1010
3Convert binary 1111 to decimal.
15
4Convert decimal 8 to binary.
1000
5Convert hexadecimal A to decimal.
10
📄 Number Systems — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.