Binary Number System
Introduction
The Binary Number System, also known as Base 2, is a mathematical system that uses only two digits: 0 and 1. While we normally count in Base 10 (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), computers and electronic devices use the Binary system to process information.
Key Points
- Meaning of Binary: It is a numbering system where every value is represented using only two symbols: 0 and 1.
- Converting Base 2 to Base 10: To change a binary number to a regular (denary) number, we multiply each digit by its place value (units, twos, fours, eights, etc.) and add them together.
- Example: 112=(1×2)+(1×1)=2+1=310.
- Converting Base 10 to Base 2: To change a regular number to binary, we divide the number by 2 repeatedly and record the remainders. The final answer is written by reading the remainders from the bottom to the top.
- Addition of Binary Numbers:
- 0+0=0
- 0+1=1
- 1+1=10 (Write 0 and carry 1 to the next column).
- Subtraction of Binary Numbers:
- 1−1=0
- 1−0=1
- 10−1=1 (This happens when you borrow 1 from the next column).
- Multiplication of Binary Numbers: This follows the same rules as Base 10 multiplication:
- 1×1=1
- 1×0=0
- 0×0=0
- Division of Binary Numbers: This is done using the long division method, similar to Base 10, but using only the digits 0 and 1.
Brief Summary
The Binary Number System is the "language of computers" consisting only of 0s and 1s. By understanding how to convert between Base 2 and Base 10, and how to perform basic operations like addition and subtraction, we can understand how digital systems calculate and store data.
