Binary Representation of IP Addresses

In binary arithmetic, each bit within a group represents a power of two. Specifically, the first bit in a group represents 20 [Editor’s note for non-math majors: mathematicians stipulate that any number raised to the power of zero equals 1], the second bit represents 21, the third bit represents 22, and so on. It’s easy to understand binary because each successive bit in a group is exactly twice the value of the previous bit.

The following table represents the value for each bit in a byte (remember, a byte is 8 bits). In binary math, the values for the bits ascend from right to left, just as in the decimal system you’re accustomed to:


8th bit 7th bit 6th bit 5th bit 4th bit 3rd bit 2nd bit 1st bit
128 (27) 64 (26) 32 (25) 16 (24) 8 (23) 4 (22) 2 (21) 1 (20)


Now that we know how to calculate the value for each bit in a byte, creating large numbers in binary is simply a matter of turning on certain bits and then adding together the values of those bits. So what does an 8-bit binary number like 01101110 represent? The following table dissects this number. Remember, a computer uses 1 to signify “on” and 0 to signify “off”:


128 (27) 64 (26) 32 (25) 16 (24) 8 (23) 4 (22) 2 (21) 1 (20)
0 1 1 0 1 1 1 0

In the table above, you can see that the bits with the values 64, 32, 8, 4 and 2 are all turned on. As mentioned before, calculating the value of a binary number means totaling all the values for the “on” bits. So for the binary value in the table, 01101110, we add together 64+32+8+4+2 to get the number 110. Binary arithmetic is pretty easy once you know what’s going on.

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