Arithmetic (Beginner) · Quick Reference

Number Systems Cheat Sheet

Arithmetic (Beginner) · Lesson 2/21

In one line: a number system is a way of writing numbers using a set of symbols and rules. Computers, in particular, rely heavily on number systems other than the everyday decimal system.

Key Ideas

1Decimal (Base-10). The system we use daily. Uses digits 0-9. Each place value is a power of 10.

2Binary (Base-2). Uses only digits 0 and 1. Each place value is a power of 2. Used inside computers.

3Octal (Base-8). Uses digits 0-7. Each place value is a power of 8.

4Hexadecimal (Base-16). Uses digits 0-9 and letters A-F (A=10 ... F=15). Each place value is a power of 16.

5Converting Between Systems. To convert any base to decimal, multiply each digit by its place value (power of the base) and add the results.

Worked Examples

Convert binary 1011 to decimal.

Convert decimal 25 to binary.

11001

Convert hexadecimal 2F to decimal.

Formulas

Decimal value = sum of (digit x base^position), counting positions from 0 on the right.

Practice Yourself

Convert binary 101 to decimal.

Convert decimal 10 to binary.

1010

Convert binary 1111 to decimal.