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As humans we have a total of 10 fingers (5 fingers on each hand). So it's only natural that our counting system is based on groups of 10. Now just imagine for a moment that humans only had 2 fingers. Would a counting system with the group of 10 be logical? Probably not. And this is the exact predicament we have with computers.
All computers are created with 2 fingers, but we refer to them as switches. They can only be in one of 2 positions: on or off. When you enter a dark room you turn the light switch on, doing so changes the switch from 0 (off) to 1 (on). This is how a computer counts.
And now it gets complicated...
Each column in our number system represents a grouping of 10. The number 13 is made of 2 parts: 10+3. Meanwhile 113 is actually 100+10+3.
In binary it's a little different (but the principle is the same). We just substitute 10 with 2. Instead of 10 we have 2, instead of 100 we have 4. So the number 3 is 11 in binary (2+1). The number 6 in binary is 110 (4+2+0).
With this in mind, take a look at the following which outlines the calculations needed to count to 31 in binary.
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