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Table Of Contents  CertiGuide to A+ (Core Hardware)
 9  Appendix A:  Decoding Math

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Base 2

At its base form, a computer only knows two things. On or off. Put in a math expression, that looks like zero or 0 and one, expressed as 1. OK. Let’s start counting.

0
1

Oops!

Your computer just ran out of fingers!

So, in base 2 math, the same trick used in base 10 is applied.

Base 2 Base 10
0 = 0
1 = 1
10 = 2
11 = 3
100 = 4
101 = 5

And just like base 10, can in theory, go on forever. Reading base 2 math to base 10 math is not difficult with a little practice. Since there are eight bits in a byte, let’s look at what 8 bits can do

128 64 32 16 8 4 2 1

Each value can be expressed in a column, just like base 10, only this is base 2. If we show each “on” bit in bold and each “off” bit in regular text, we can count in binary as follows:

128 64 32 16 8 4 2 1 = 1
128 64 32 16 8 4 2 1 = 2
128 64 32 16 8 4 2 1 = 2+1 = 3
128 64 32 16 8 4 2 1 = 4
128 64 32 16 8 4 2 1 = 4 + 1 = 5

And so on. Now the maximum one can do with 8 bit or a byte is:

128 64 32 16 8 4 2 1 = 255

Of course you can get any combination between 0 and 255 by selecting which value you want to turn on or off.

Maybe now you realize why you so often see subnet masks that contain the values 255 and 0.


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