Binary to Decimal Conversion Explained Simply — With Free Converter

Binary to decimal conversion is one of the fundamental concepts in computer science that every engineering student, programmer, and IT professional needs to understand. Whether you're preparing for GATE, campus placements, or learning programming, this guide will make binary conversion crystal clear.

What Is Binary Number System?

The binary number system uses only two digits: 0 and 1. It's the language computers understand — every piece of data your computer processes is ultimately represented in binary. Each digit in a binary number is called a bit (binary digit).

Binary to Decimal Conversion Method

To convert binary to decimal, multiply each bit by 2 raised to its position power (starting from 0 on the right), then add all the results.

Example: Convert 1101 (binary) to decimal

Position	3	2	1	0
Binary digit	1	1	0	1
Power of 2	2³=8	2²=4	2¹=2	2⁰=1
Calculation	1×8=8	1×4=4	0×2=0	1×1=1

Result: 8 + 4 + 0 + 1 = 13

So, 1101 in binary equals 13 in decimal.

More Examples

• 1010 = (1×8) + (0×4) + (1×2) + (0×1) = 8 + 0 + 2 + 0 = 10
• 11111 = 16 + 8 + 4 + 2 + 1 = 31
• 100000 = 32 + 0 + 0 + 0 + 0 + 0 = 32
• 11111111 = 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255

Quick Reference: Powers of 2

Power	2⁰	2¹	2²	2³	2⁴	2⁵	2⁶	2⁷	2⁸
Value	1	2	4	8	16	32	64	128	256

Why Binary Matters in Computer Science

• All computer memory is stored in binary (RAM, SSD, HDD)
• Network IP addresses use binary (IPv4 is 32 bits, IPv6 is 128 bits)
• Assembly language and low-level programming use binary operations
• Understanding binary is essential for GATE CSE, campus placements, and coding interviews

Frequently Asked Questions

What is the largest decimal number in 8-bit binary?

The largest unsigned 8-bit binary number is 11111111, which equals 255 in decimal. For signed 8-bit numbers using two's complement, the range is -128 to 127.

How do computers use binary?

Computers use binary because electronic circuits have two states: on (1) and off (0). All data — text, images, videos, and programs — is stored and processed as sequences of 1s and 0s at the hardware level.

Is binary to decimal conversion asked in GATE exams?

Yes, number system conversions (binary, decimal, octal, hexadecimal) are commonly tested in GATE CSE and other competitive exams like UGC NET, ISRO, and campus placements for IT companies.

What is the binary of 100?

100 in decimal is 1100100 in binary. You can verify: 64+32+4 = 100. Use our free converter to check any binary-to-decimal or decimal-to-binary conversion.

What is the difference between binary, octal, decimal and hexadecimal?

These are number systems with different bases: Binary (base-2, digits 0-1), Octal (base-8, digits 0-7), Decimal (base-10, digits 0-9), Hexadecimal (base-16, digits 0-9 and A-F). Computers primarily use binary internally, while hexadecimal is commonly used in programming.