Step 1 — Binary Fundamentals
Binary is the foundation of subnetting. Before touching IP addresses, you need to understand how binary works. This step teaches you from absolute zero — no prior knowledge required.
What is Binary?
Binary is a number system that uses only two digits: 0 and 1. Every number we use in networking can be represented in binary.
Computers use binary because they store information as on/off switches. Each switch is a bit — either 0 (off) or 1 (on).
Why 8 Bits = 255
An octet is exactly 8 bits. With 8 switches, you can create 256 different combinations (2⁸ = 256). Since we start counting at 0, the range is 0 to 255.
Minimum: 00000000 = 0
Maximum: 11111111 = 255
Total combinations: 256 (0-255)
Binary Place Values
Just like decimal has place values (ones, tens, hundreds), binary has place values. Each position doubles as you move left.
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 2⁷ | 2⁶ | 2⁵ | 2⁴ | 2³ | 2² | 2¹ | 2⁰ |
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
Memorize these values: 128, 64, 32, 16, 8, 4, 2, 1. This pattern appears constantly in subnetting.
Converting Decimal to Binary
To convert a decimal number to binary, start from the left and ask: "Can this place value fit?" If yes, put a 1 and subtract. If no, put a 0.
Example: Convert 192 to binary
- 192 ≥ 128? Yes → write 1, remainder = 192 - 128 = 64
- 64 ≥ 64? Yes → write 1, remainder = 64 - 64 = 0
- 0 ≥ 32? No → write 0
- 0 ≥ 16? No → write 0
- 0 ≥ 8? No → write 0
- 0 ≥ 4? No → write 0
- 0 ≥ 2? No → write 0
- 0 ≥ 1? No → write 0
Result: 192 = 11000000
Example: Convert 85 to binary
- 85 ≥ 128? No → write 0
- 85 ≥ 64? Yes → write 1, remainder = 85 - 64 = 21
- 21 ≥ 32? No → write 0
- 21 ≥ 16? Yes → write 1, remainder = 21 - 16 = 5
- 5 ≥ 8? No → write 0
- 5 ≥ 4? Yes → write 1, remainder = 5 - 4 = 1
- 1 ≥ 2? No → write 0
- 1 ≥ 1? Yes → write 1, remainder = 1 - 1 = 0
Result: 85 = 01010101
Converting Binary to Decimal
Add up the place values where there's a 1.
Example: Convert 11001100 to decimal
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 |
Add the place values where there's a 1:
128 + 64 + 8 + 4 = 204
Practice Exercises
Do these now. Don't skip ahead until you can solve them quickly.
1. Convert to binary:
- 255
- 128
- 64
- 224
- 10
2. Convert to decimal:
- 10110101
- 11001111
- 00111100
- 10011001
- 01011010
Show Answers
1. Decimal to Binary:
- 255 = 11111111
- 128 = 10000000
- 64 = 01000000
- 224 = 11100000
- 10 = 00001010
2. Binary to Decimal:
- 10110101 = 181 (128 + 32 + 16 + 4 + 1)
- 11001111 = 207 (128 + 64 + 8 + 4 + 2 + 1)
- 00111100 = 60 (32 + 16 + 8 + 4)
- 10011001 = 153 (128 + 16 + 8 + 1)
- 01011010 = 90 (64 + 16 + 8 + 2)
Checkpoint
Before moving to Step 2, make sure you can:
- Explain why 8 bits gives us 0-255 (256 values)
- Recite the place values from memory: 128, 64, 32, 16, 8, 4, 2, 1
- Convert any decimal (0-255) to binary without hesitation
- Convert any 8-bit binary back to decimal
If any of these feel shaky, practice more. Subnetting builds on this foundation.