Binary Number Chart- Conversion and Counting System Guide

What the Hell Is Binary Anyway?

Binary is a counting system that uses only two digits: 0 and 1. That's it. No 2s, no 3s, no 9s. Just off and on, true and false, yes and no.

Computers run on binary because electronic circuits have two states: powered or not powered. It's the simplest way to represent data at the hardware level. Every image, video, text file, and app on your device exists as a string of 0s and 1s.

You need to understand this if you're learning programming, working with networking, or just trying to decode what tech people are talking about.

The Binary Number Chart You Actually Need

Here's a direct conversion table for numbers 0 through 15. Memorize this and you'll understand binary at a glance.

Each group of four binary digits is called a nibble. Two nibbles make a byte. That's why hex exists—it shorthand for binary. Four binary digits = one hex digit. Much cleaner to read.

How Binary Place Values Work

Decimal uses powers of 10. Binary uses powers of 2. That's the only difference.

In decimal, the number 347 breaks down as:

• 3 × 100 (10²) = 300
• 4 × 10 (10¹) = 40
• 7 × 1 (10⁰) = 7

In binary, the number 1101 breaks down as:

• 1 × 8 (2³) = 8
• 1 × 4 (2²) = 4
• 0 × 2 (2¹) = 0
• 1 × 1 (2⁰) = 1

8 + 4 + 0 + 1 = 13

That's the whole trick. Each position doubles going left. 1, 2, 4, 8, 16, 32, 64, 128, 256, and so on.

How to Convert Decimal to Binary

Use the division method. It's mechanical and foolproof.

1. Divide the number by 2
2. Write down the remainder (0 or 1)
3. Divide the quotient by 2
4. Repeat until the quotient is 0
5. Read the remainders from bottom to top

Let's convert 42 to binary:

• 42 ÷ 2 = 21 remainder 0
• 21 ÷ 2 = 10 remainder 1
• 10 ÷ 2 = 5 remainder 0
• 5 ÷ 2 = 2 remainder 1
• 2 ÷ 2 = 1 remainder 0
• 1 ÷ 2 = 0 remainder 1

Read bottom to top: 101010

Verify: 32 + 8 + 2 = 42. Correct.

Quick Method for Powers of 2

If a number is a power of 2, the binary is simple. Just put a 1 in that position and 0s everywhere else.

• 8 in decimal = 1000 in binary
• 16 in decimal = 10000 in binary
• 64 in decimal = 1000000 in binary

That's useful for subnet masks, bit flags, and memory addresses.

How to Convert Binary to Decimal

Multiply each bit by its place value and add them up. That's it.

Convert 100101 to decimal:

• Position 5: 1 × 32 = 32
• Position 4: 0 × 16 = 0
• Position 3: 0 × 8 = 0
• Position 2: 1 × 4 = 4
• Position 1: 0 × 2 = 0
• Position 0: 1 × 1 = 1

32 + 4 + 1 = 37

Some people find it easier to identify the powers of 2 first, then sum them. For 100101: that's 32 + 4 + 1. Done.

Counting in Binary

Binary counting follows the same rules as decimal, but you flip to the next column more often. Watch the pattern:

• 0, 1, 10, 11, 100, 101, 110, 111, 1000...

Notice when you run out of digits (you can only use 1), you carry over to the next column. Same as decimal, but it happens every two counts instead of every ten.

This is exactly how computers count internally. They increment registers by adding 1 to the binary value. Everything is math at the lowest level.

Where You'll Actually Use This

IP Addresses and Subnetting

IPv4 addresses are 32-bit binary numbers. The subnet mask determines network vs host bits. You need binary to understand CIDR notation and why 255.255.255.0 divides the way it does.

Bit Flags and Permissions

Unix file permissions use bit flags: read=4, write=2, execute=1. Add them up for permission sets. chmod 755 means rwxr-xr-x (4+2+1=7 for owner, 4+1=5 for group and others).

Hex Color Codes

#FF5733 breaks down as RGB(255, 87, 51). Each hex pair is 8 bits. FF = 11111111 = 255. This is why hex is the standard for web colors.

Debugging and Low-Level Programming

Memory addresses, register values, and network packets are all binary. When something breaks at the hardware level, you'll need to read hex dumps and binary logs.

Common Mistakes That Waste Time

• Confusing binary and decimal — "10" means ten in decimal, but two in binary. Always clarify the base.
• Forgetting leading zeros — 0011 and 11 are the same value, but the leading zeros matter in fixed-width contexts like network masks.
• Misreading place values — The rightmost bit is 2⁰, not 2¹. People flip this constantly.
• Overcomplicating conversions — The math is basic. Division remainders or place value multiplication. No tricks needed.

Quick Reference: Common Binary Values

The Bottom Line

Binary isn't complicated. It's just counting with two fingers instead of ten. The place value system is identical to decimal—same logic, different base. Once that clicks, conversions become trivial.

You don't need to memorize every binary number from 0 to 65535. Know the powers of 2, understand the conversion methods, and recognize common patterns. That's enough for 99% of real work.