In modern networking, you will rarely perform subnet math by hand, as tools and calculators automate the process. However, understanding the manual conversion between decimal and binary is crucial for networking interviews, certification exams, and gaining a deeper understanding of how IP addressing works. This lesson provides some simple cheats to help you master it.
First, it's highly beneficial to memorize the base-2 calculations, as they form the foundation of binary math.
- 2^1 = 2
- 2^2 = 4
- 2^3 = 8
- 2^4 = 16
- 2^5 = 32
- 2^6 = 64
- 2^7 = 128
- 2^8 = 256
The Binary Conversion Chart
To easily convert numbers, we use a chart that represents the value of each bit in an 8-bit octet of an IP address.
1 1 1 1 1 1 1 1
128 64 32 16 8 4 2 1This chart is your primary tool. Each number corresponds to a bit's position. The full sum, 128+64+32+16+8+4+2+1, equals 255, which is the highest possible value in an octet.
Decimal to Binary Conversion
Let's convert the IP address 192.168.23.43 to binary. We'll walk through the first octet, 192, to demonstrate the process. We use the values from our chart: 128 64 32 16 8 4 2 1.
- Start with the number
192. Can you subtract 128 from it? Yes (192 - 128 = 64). So, the first bit is 1. - Our new number is
64. Can you subtract the next value, 64, from it? Yes (64 - 64 = 0). The second bit is 1. - Our remainder is now
0. We cannot subtract 32, 16, 8, 4, 2, or 1. Therefore, the remaining bits are all 0.
The binary form of 192 is 11000000. You can apply this same subtraction method to the other octets.
Binary to Decimal Conversion
To convert from binary back to decimal, you simply add the values from the chart where a 1 appears in the binary number. Let's convert 11000000 back to decimal.
Looking at the chart 128 64 32 16 8 4 2 1, the first two bits are 1. This means we add the first two values:
128 + 64 = 192
Since all other bits are 0, we don't add any other values. The formula 128 + 64 + 0 + 0 + 0 + 0 + 0 + 0 gives us 192. It's that simple!