Overview
This lecture covers the basics of binary and other number bases, explaining how they work and how to convert between different bases.
What Are Number Bases?
- A number base or numeral system defines how numbers are represented using a set of symbols (digits).
- Base 10 (decimal) is the standard system, using digits 0–9.
- Binary (base 2) uses only two digits: 0 and 1.
- Other common bases include octal (base 8) and hexadecimal (base 16).
Binary System
- Each binary digit is called a bit and represents a power of 2.
- Numbers are written using only 0s and 1s; for example, 1011₂ equals 11 in decimal.
- To convert binary-to-decimal, multiply each bit by its place value (2ⁿ) and add them.
Converting Between Bases
- To convert from another base to decimal, multiply each digit by its base power and sum the results.
- To convert from decimal to another base, repeatedly divide by the base and record the remainders.
Other Bases
- Octal uses digits 0–7, with each place representing a power of 8.
- Hexadecimal uses digits 0–9 and letters A–F, representing values 0–15, with each place a power of 16.
Key Terms & Definitions
- Binary — Number system with base 2, using digits 0 and 1.
- Decimal — Standard number system with base 10, digits 0–9.
- Octal — Number system with base 8, digits 0–7.
- Hexadecimal — Number system with base 16, digits 0–9 and A–F.
- Bit — A single binary digit (0 or 1).
- Place Value — The value of a digit based on its position and the base.
Action Items / Next Steps
- Practice converting numbers between binary, decimal, octal, and hexadecimal systems.
- Review homework or assigned readings on number base conversions.