How to Count in Binary: A Simple Tutorial for Complete Beginners

Published January 17, 2025 • 10 min read

Think counting in binary is complicated? It's actually easier than you think! In this tutorial, you'll learn how to count from 0 to 100 (and beyond) in binary. By the end, you'll understand exactly how computers count — and you might even find it fun.

What is Binary? (The 30-Second Version)

Binary is a number system that uses only two digits: 0 and 1.

That's it! While our normal counting system (called "decimal") uses ten digits (0-9), binary uses just two. It's also called "base-2" because it's based on powers of 2.

Computers use binary because electronic circuits have two states: on (1) or off (0). It's the simplest system to implement in hardware.

The Secret to Understanding Binary: Position Values

In our everyday decimal system, each position represents a power of 10:

1000 = 10³ = Thousands
100 = 10² = Hundreds
10 = 10¹ = Tens
1 = 10⁰ = Ones

Binary works the same way, but with powers of 2 instead:

128 = 2⁷
64 = 2⁶
32 = 2⁵
16 = 2⁴
8 = 2³
4 = 2²
2 = 2¹
1 = 2⁰

Each position to the left doubles in value. That's the only rule you need to remember!

Counting from 0 to 15 in Binary

Let's start counting! I'll show you the pattern, and you'll see how simple it is.

Decimal	Binary	How to Think About It
0	0000	Nothing
1	0001	Just 1
2	0010	One 2, zero 1s
3	0011	One 2 + one 1 = 3
4	0100	One 4
5	0101	One 4 + one 1 = 5
6	0110	One 4 + one 2 = 6
7	0111	One 4 + one 2 + one 1 = 7
8	1000	One 8
9	1001	One 8 + one 1 = 9
10	1010	One 8 + one 2 = 10
11	1011	One 8 + one 2 + one 1 = 11
12	1100	One 8 + one 4 = 12
13	1101	One 8 + one 4 + one 1 = 13
14	1110	One 8 + one 4 + one 2 = 14
15	1111	One 8 + one 4 + one 2 + one 1 = 15

💡 Pro Tip: See the Pattern?

Binary counting follows the same pattern as decimal! When you run out of digits (after 1), you add a new position to the left and reset everything to the right. In decimal, after 9 comes 10. In binary, after 1 comes 10 (which equals 2 in decimal).

The Easy Way to Count in Binary

Here's a simple rule that makes binary counting effortless:

Start with 0
Flip the rightmost 0 to 1 (or 1 to 0 if it's already 1)
If you just flipped a 1 to 0, keep flipping digits to the left until you flip a 0 to 1

Example: Counting from 5 to 8

5 = 0101
→ Flip rightmost: 0110 = 6

6 = 0110
→ Flip rightmost: 0111 = 7

7 = 0111
→ Flip right (1→0), keep going (1→0), keep going (1→0), flip (0→1)
→ Result: 1000 = 8

Counting to 100 in Binary (and Beyond!)

Let's jump to some bigger numbers to show you the pattern continues:

Decimal	Binary	Breakdown
16	00010000	16
25	00011001	16 + 8 + 1
50	00110010	32 + 16 + 2
75	01001011	64 + 8 + 2 + 1
100	01100100	64 + 32 + 4
127	01111111	64 + 32 + 16 + 8 + 4 + 2 + 1
255	11111111	All 8 bits ON!

Why is 255 Special?

With 8 binary digits (bits), the largest number you can represent is 11111111 in binary, which equals 255 in decimal. This is why you see 255 so often in computing: RGB color values (0-255), subnet masks (255.255.255.0), and byte values all max out at 255!

Quick Reference: Powers of 2 (Memorize These!)

If you memorize these common powers of 2, binary counting becomes instant:

2⁰ = 1
2¹ = 2
2² = 4
2³ = 8
2⁴ = 16
2⁵ = 32
2⁶ = 64
2⁷ = 128
2⁸ = 256
2⁹ = 512
2¹⁰ = 1,024 (roughly 1 kilobyte!)

Practice Exercise: Count These in Binary!

Try converting these numbers to binary yourself before looking at the answers:

What is 20 in binary?
What is 31 in binary?
What is 64 in binary?

Answers

1. 20 = 10100 (16 + 4)
2. 31 = 11111 (16 + 8 + 4 + 2 + 1)
3. 64 = 1000000 (just one 64!)

Why Learning Binary Counting Matters

For Programmers

Understanding bitwise operations (AND, OR, XOR, shifts)
Working with permissions and flags
Optimizing memory usage
Debugging low-level code

For Computer Science Students

Foundation for computer architecture courses
Understanding how data is stored
Binary arithmetic and logic gates
Acing technical interviews

For Everyone Else

Appreciate how computers actually work
Understand the digital world better
Impress your friends at parties (seriously!)
It's actually kind of fun once you get it

🎯 Want to Practice Daily?

Get a binary clock from Binesse! Every time you check the time, you're practicing binary conversion. It's the most natural way to master binary counting — you'll be fluent in weeks.

Common Mistakes (and How to Avoid Them)

Mistake 1: Forgetting Position Values

Wrong: Thinking 1010 is "one thousand and ten"
Right: 1010 is 8 + 2 = 10 in decimal

Mistake 2: Reading Right-to-Left Wrong

Remember: the rightmost digit is always the "ones" place (2⁰). Position values increase as you move left, just like in decimal.

Mistake 3: Giving Up Too Early

Binary seems weird at first because it's unfamiliar. But it's actually simpler than decimal — only two digits to remember! Give yourself a few practice sessions and it clicks.

Next Steps: Keep Learning!

Now that you can count in binary, you're ready to explore: