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What is the Binary Number System?

Visual representation of binary digits with 0s and 1s
Binary digits - the building blocks of computer language

The binary number system is how computers understand and process information. Unlike our decimal system that uses 10 digits (0-9), binary uses only two digits: 0 and 1.

Why only two digits? Computers use electricity to work, and it's easier to represent information with just two states:

0 = OFF (no electricity)
1 = ON (electricity flowing)

Each binary digit is called a bit. A group of 8 bits is called a byte, which can represent a single character like 'A' or '7'.

How the Binary System Works

Place value system of binary numbers
Binary place values compared to decimal place values

In binary, each digit's position represents a power of 2, starting from the right:

128
64
32
16
8
4
2
1

To find the decimal value of a binary number:

1. Write the binary digits
2. Multiply each digit by its place value
3. Add all the results together

Example: Binary 1011
= (1×8) + (0×4) + (1×2) + (1×1)
= 8 + 0 + 2 + 1
= 11 in decimal

Binary Conversion Methods

Binary to decimal and decimal to binary conversion process
Converting between binary and decimal systems

Decimal to Binary Conversion

To convert a decimal number to binary:

1. Divide the number by 2
2. Write down the remainder (0 or 1)
3. Divide the quotient by 2 again
4. Repeat until the quotient is 0
5. The binary number is the remainders read 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

Binary to Decimal Conversion

To convert binary to decimal:

1. Write down the place values (1,2,4,8,16,... from right)
2. Multiply each binary digit by its place value
3. Add all the products together

Example: Convert 10101 to decimal
Place values: 16, 8, 4, 2, 1
Calculation: (1×16) + (0×8) + (1×4) + (0×2) + (1×1) = 16+0+4+0+1 = 21

Try It Yourself!

Binary result will appear here
Decimal result will appear here

Real-World Examples

Binary representations of common computer elements
How computers use binary in everyday applications

Binary is used everywhere in computing:

1. Text Representation: Each letter has a binary code. For example:

'A' = 01000001
'B' = 01000010
'C' = 01000011
2. Images: Pictures are made of tiny dots (pixels). Each pixel's color is stored as binary numbers.

3. Sound: Music and sounds are converted to binary by measuring sound waves many times per second.

4. Computer Programs: All software and apps are written using binary instructions that tell the computer what to do.

5. Data Storage: Your files, photos, and videos are all stored as long sequences of 0s and 1s on your device.

Binary Numbers Quiz

Test your understanding with this 5-question quiz. Choose the correct answer for each question.

1. How many digits are in the binary number system?
2. What is the decimal equivalent of binary 1100?
3. What is the binary equivalent of decimal 7?
4. What do we call a group of 8 binary digits?
5. Why do computers use binary?

Frequently Asked Questions

Here are answers to common questions about binary numbers:

Computer Number Trivia

Discover interesting facts about numbers in computing:

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