easy compsci question?

Question

How many different numbers can be represented by 3 bits?

Sorry I dont really get this question...the answer is 8 but why? I thought 1 bit can only represent one number? Someone please help >///<

Answer 1

Bits are in binary language.

Three bits will give you a binary number of 111. The least significant digit is the ones column, next left is the base or twos column and the far left is 2^2 or 4 if the bit is set. So you have 1 in the ones col plus a 2 that is represented by a 1 in the twos col and a 4 as represented by a 1 in the 2^2 column.

So it is 4+2+1=7 in binary. We have discussed all bit set to give you a seven but if all bits are clear it is 0+0+0=0 and that is considered another number.

There are a ton of ways to teach this and I have taught most of them.

Here is a second way

000 = 0 base 10
001 = 1 base 10
010 = 2 base 10
011 = 3 base 10
100 = 4 base 10
101 = 5 base 10
110 = 6 base 10
111 = 7 base 10
Now that is all possible combinations of 1s and 0s possible in three bits. So it is 1 thru 7 plus 0 makes 8.

I can do this for hours, and I am available through my profile. WARNING I will teach you for hours but I will not do your homework for you.

Answer 2

Well, here ya go...
3 bits could represent 8 distinct bit patterns because 2 to the 3rd power = 8 (2x2x2 = 8).
The two comes from the binary system, having two posibilities.

here are the bit patterns which would represent the numbers 0 thru 7...

000 = 0
001 = 1
010 = 2
011 = 3
100 = 4
101 = 5
110 = 6
111 = 7

Hope it's a little clearer.