Binary
Binary is a base-2 numbering system that consists of only two digits: 0 and 1. It serves as the fundamental language of computers, as digital systems rely on binary to process, store, and transmit data.
Binary comes from electronic device - transistor. Binary 0 indicates that there is no voltage, binary 1 indicates that there is voltage.
Why is Binary Important?
Foundation of Computing – All digital devices operate using binary logic.
Efficient Data Processing – Computers interpret electrical signals as ON (1) and OFF (0).
Universal Standard – Binary is used in memory, processors, networks, and software development.
The Binary Number System
Unlike the decimal system (base-10), which uses digits from 0 to 9, the binary system (base-2) uses only 0s and 1s. Each digit in a binary number, called a bit, represents a power of 2.
Example:
The binary number 1011 converts to 11 in decimal:
1 x 2^3 + 0 x 2^2 + 1 x 2^1 + 1 x 2 = 11
🔹 Decimal to Binary Conversion
Divide the decimal number by 2.
Write down the remainder (0 or 1).
Repeat until the quotient becomes 0.
Read the remainders from bottom to top to get the binary number.
Example: Convert 19 to binary:
19 ÷ 2 = 9 remainder 1
9 ÷ 2 = 4 remainder 1
4 ÷ 2 = 2 remainder 0
2 ÷ 2 = 1 remainder 0
1 ÷ 2 = 0 remainder 1
Binary: **10011**
Binary Arithmetic
Binary numbers follow specific rules for addition, subtraction, multiplication, and division.
Binary Addition
Binary addition is similar to decimal addition, with the following rules:
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 10 (carry 1)
1011
+ 1101
------------
11000
Binary Subtraction
Binary subtraction follows borrowing rules similar to decimal subtraction:
0 - 0 = 0
1 - 0 = 1
1 - 1 = 0
0 - 1 = 1 (borrow from the left)
Binary Multiplication
Binary multiplication operates like decimal multiplication but only involves 0s and 1s:
0 × 0 = 0
0 × 1 = 0
1 × 0 = 0
1 × 1 = 1
Example:
101
× 011
------------
101
101
------------
1111
Binary Division
Binary division follows the same principles as long division in decimal numbers.
Applications of Binary
Computer Memory & Storage – Data is stored as binary (0s and 1s).
Processing (CPU Operations) – Binary arithmetic is used in logic circuits.
Networking & Communication – IP addresses and data transmission rely on binary.
Programming & Software Development – Binary logic underpins coding and algorithms.
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