What is Binary?

Binary is a number system that uses only two digits: 0 and 1. This system is called “base-2,” compared to the decimal system (base-10) we commonly use, which has digits from 0 to 9.
Computers use binary because electronic circuits only have two states: on (1) and off (0). By combining sequences of these two states, computers perform calculations, store information, and execute programs.

Understanding Binary Numbers

Just like in decimal, where each digit represents a power of 10, in binary, each digit represents a power of 2.

Example: The binary number 1011 can be converted to decimal as follows:

1 × 2^3 = 8
0 × 2^2 = 0
1 × 2^1 = 2
1 × 2^0 = 1
Total = 8 + 0 + 2 + 1 = 11 (decimal)

Converting Between Binary and Decimal

• Binary to Decimal: Multiply each binary digit by its corresponding power of 2 and sum the results.
• Decimal to Binary: Continuously divide the decimal number by 2, recording the remainders from bottom to top.

Example (Convert 13 to binary):

13 ÷ 2 = 6 remainder 1
6 ÷ 2 = 3  remainder 0
3 ÷ 2 = 1  remainder 1
1 ÷ 2 = 0  remainder 1
Binary:    1101

How to Learn Binary Effectively

1. Practice Conversions: Convert numbers back and forth between binary and decimal.
2. Use Online Tools: Try binary calculators and interactive number converters.
3. Memorize Small Binary Values: Knowing common numbers (0-15) in binary can help speed up calculations.
4. Understand Binary Operations: Learn basic operations like addition, subtraction, and bitwise operations (AND, OR, XOR).
5. Apply to Real-World Scenarios: Study how binary is used in networking (IP addresses), storage (file sizes), and programming (bit manipulation).
6. Use Mnemonics & Patterns: Recognizing patterns in binary numbers makes learning easier.

Common Uses of Binary

• Computers & Processors: Everything from arithmetic calculations to decision-making in CPUs operates in binary.
• Data Storage: Hard drives and memory store information as sequences of 0s and 1s.
• Networking: IP addresses and subnet masks rely on binary numbers.
• Programming: Many programming languages use binary for bitwise operations.