I need Help!!!!! Binary Numbers???? 10 POINTS?

Question

Ok so were talking about old number systems. And we have to investigate them. It includes the binary system. I'M IN MIDDLE SCHOOL! i need someone to explain this to me!!!!! ive looked on websites but its WAY to complicated!!!!!

Please help!!

Answer 1

We have ten fingers and so we evolved into a number system with ten digits:  0, 1, 2, 3, 4, 5, 6, 7, 8, 9.  Larger numbers use combinations of 0 through 9.  The whole number after 9 is 10 or ten.

If we only had two fingers we might have evolved into a number system with only two digits: 0 and 1.  Larger numbers would be combinations of 0 and 1.  The  whole number after 1 would be 10, but it is equivalent to two.

Answer 2

It is similar to the decimal system that we use, but we would only use 2 numbers. 0 and 1. It is the systems that computers use. Computers only understand 0 and 1. In decimal you would count from 0 to 9 then you move into the teens and go from 10 to 19, so you use the same 10 previous numbers and then add a 1 before them then into the 20's with the same basic 10 numbers with a 2 before them, 20 to 29. Once you get to 99 you start all over again, you add a 1 ahead of 00 and so on. Binary would go like this.

00 for 0

01 for 1

10 for 2

11 for 3 now you are out of number, so you add one more, just like in decimal.and star all over again.

100 for 4

101 for 5

110 for 6

111 for 7 and so on.

I hope this helps and you understand.

Answer 3

Actually, there is nothing "old" about the binary number system. The machine you're using to read this -- guess what number system(s) it uses? (Those old Roman computers used a different system. :)

In any number system, each place, counting from the right, stands for some particular number. For the decimal number system, in the number 496, 6 is the number of 1s, 9 the number of 10s, and 4 the number of 100s. So 496 is 4 hundreds, plus 9 tens, plus 6 ones.

In binary, the first (again fron the right) is the number of 1s; the second the number of 2s, the third the number of 4s, then 8s, 16s, 32s, etc. That is, every place doubles (instead of multiples of 10 like the decimal system). And there are only two digits -- 0 and 1. So the binary number 1010 is 1 eight, 0 fours, 1 two, and no ones-- that is,  8+2 = 10.

If you understand exponents, every position is a base (such as 10, or 2, or 8, or 16) raised to a power. The rightmost digit is to the 0th power, the next to the 1st power, the third position is to the second power, and so on:

b^n, b^n-1, ..., b^3, b^2, b^1, b^0

So our decimal number system is:

...10^3, 10^2, 10^1, 10^2

(i.e., 1000, 100, 10, 1)

Whereas the binary number system is:

..., 2^3, 2^2, 2^1, 2^0

(i.e., 8, 4, 2, 1)