Base 2 Binary- Complete Beginner's Guide

What the Hell Is Binary?

Binary is a number system with only two digits: 0 and 1. That's it. Nothing fancy. You already know the decimal system—the one humans use every day. It has ten digits (0-9). Binary just cuts that in half. Two digits instead of ten. Computers use binary because hardware is dumb. A switch is either on (1) or off (0). Billions of switches flipping on and off. That's all your photos, videos, and this article amounts to.

How Binary Numbers Actually Work

In decimal, each position represents a power of 10:

1 = 10⁰
10 = 10¹
100 = 10²
1,000 = 10³

Binary follows the same logic, but each position is a power of 2:

1 = 2⁰ = 1
10 = 2¹ = 2
100 = 2² = 4
1000 = 2³ = 8
10000 = 2⁴ = 16
100000 = 2⁵ = 32

Each 1 in a binary number means "include this place value." Each 0 means "skip it."

Reading Binary: A Real Example

Take the binary number 10110. Read it right to left.

Binary Digit	Place Value	Calculation	Decimal Value
1 (rightmost)	2⁰	1 × 1	1
1	2¹	1 × 2	2
0	2²	0 × 4	0
1	2³	1 × 8	8
1 (leftmost)	2⁴	1 × 16	16

Add them up: 16 + 8 + 0 + 2 + 1 = 27 So 10110 in binary = 27 in decimal. ✅

Converting Decimal to Binary

There's a simple division method:

Divide the decimal number by 2
Write down the remainder (0 or 1)
Divide the quotient by 2
Repeat until the quotient is 0
Read the remainders bottom to top

Example: Convert 45 to Binary

45 ÷ 2 = 22 remainder 1
22 ÷ 2 = 11 remainder 0
11 ÷ 2 = 5 remainder 1
5 ÷ 2 = 2 remainder 1
2 ÷ 2 = 1 remainder 0
1 ÷ 2 = 0 remainder 1

Read bottom to top: 101101 Check: 32 + 8 + 4 + 1 = 45 ✅

Binary Addition (The Short Version)

You only need four rules:

Input	Result
0 + 0	0
0 + 1	1
1 + 0	1
1 + 1	0 (carry 1)

When 1 + 1 happens, you write 0 and pass a 1 to the next column. This is called a carry bit. Example: 101 + 011

Working right to left:

Column 1: 1 + 1 = 0, carry 1
Column 2: 0 + 1 + carry 1 = 0, carry 1
Column 3: 1 + 0 + carry 1 = 0, carry 1
Column 4: carry 1 drops to the result

Result: 1000 (which is 8 in decimal)

Bits and Bytes: What You Actually Need to Know

Bit = a single binary digit (0 or 1)
Byte = 8 bits
A byte can represent values from 0 to 255 (2⁸ - 1)

That's why file sizes, RAM, and storage come in powers of two. 1KB = 1024 bytes, not 1000. Blame computer scientists who couldn't do math the easy way.

Common Binary Numbers Worth Memorizing

Binary	Decimal	Power of 2
1	1	2⁰
10	2	2¹
100	4	2²
1000	8	2³
10000	16	2⁴
100000	32	2⁵
1000000	64	2⁶
10000000	128	2⁷
11111111	255	2⁸ - 1

Getting Started: Your First Exercises

Practice converting these without a calculator:

Convert 63 to binary
Convert 11001 to decimal
Add 1100 + 1011

Answers at the bottom 👇

How to Check Your Work

Use Windows Calculator in programmer mode, or Google "binary to decimal converter." Don't waste time doing this by hand in production code—understand the concept, then let tools handle the grunt work.

Where Binary Shows Up in Real Life

You encounter binary whether you realize it or not:

IPv6 addresses — those long hex strings are just binary in disguise
RGB color codes — #FF0000 is a byte for red (255,0,0)
Unicode/UTF-8 — every character has a binary code point
Permissions in Linux — chmod 755 uses octal (binary in groups of three)

Understanding binary makes these things click instead of looking like random gibberish.

Answers to Exercises

63 = 111111 (64 - 1)
11001 = 25 (16 + 8 + 1)
1100 + 1011 = 10111 (12 + 11 = 23)