Counting in Binary

What you'll learn: How to count from 0 to 15 using only 1s and 0s, and spot the patterns that make binary predictable.

The Core Idea

Counting in binary follows the same principle as counting in decimal (our normal base-10 system), but you only have two digits available: 0 and 1. Just like when you reach 9 in decimal, you roll over to 10, in binary when you reach 1, you roll over to 10.

Think of it like an odometer that can only display 0 or 1 in each position. When a digit maxes out, it resets to 0 and adds 1 to the left.

Counting 0 to 15

Here's how binary counting works:

0  = 0000
1  = 0001
2  = 0010
3  = 0011
4  = 0100
5  = 0101
6  = 0110
7  = 0111
8  = 1000
9  = 1001
10 = 1010
11 = 1011
12 = 1100
13 = 1101
14 = 1110
15 = 1111

Patterns to Notice

The rightmost bit (called the "least significant bit") alternates with every count: 0, 1, 0, 1, 0, 1...

The second bit from right alternates every two counts: 00, 11, 00, 11...

The third bit alternates every four counts: 0000, 1111, 0000, 1111...

The leftmost bit alternates every eight counts.

Each position to the left changes half as frequently as the position to its right. This pattern makes binary counting systematic and predictable—once you see it, you can count to any number!

Key Takeaway: Binary counting uses only 0s and 1s, with each digit position alternating at half the frequency of the position to its right, creating a reliable pattern that computers use for all counting operations.