Can anyone give me a quick rundown on binary numbers?

Answer 1

Binary number system is just like any number system - it has a base which is equal to number of unique digits in that number system. For example:

Decimal Number System has a base of 10 and it has digits from 0-9 (total no of digits = 10 = base). The number system starts with 0 and goes up to the max digit in the number system. Then the digit at that position becomes zero and the number at higher position becomes one. Let's see if you can follow this by looking at decimal no system first
01, 02, 03, 04, 05, 06, 07, 08, 09 (now the no at least posn is 9 = max possible in a decimal no system, so this posn becomes zero and the no at the next higher level becomes 1)... therefore, after 09 (which is same as 9), you get 10.

Now use the same logic for creating binary numbers (or any no system - octal, hex), just remember binary no. system has only two digits (binary = two) -> 0 and 1... therefore the binary nos go like this (taking 3 leading zeros and keeping in mind that leading zero do not alter the value of a number, eg 09 is same as 9 and 090 is same as 90, similarly for binary 0001 = 1, 0010 =10)
0000, 0001 - least posn = 1 = max digit in binary no system, so next time we change this to zero and increment the next higher posn with 1 - so we get --- 0010
Now increment the least posn by 1, we get ---- 0011
Since both, least n next higher posn is max =1 each, so we make them both zero and the third higher posn = 1 we get -- 0100

and so on we continue - 0100, 0101, 0110, 0111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111.

Finally - the binary nos and their decimal values:
0000 = 0
0001 = 1
0010 = 2
0011 = 3
0100 = 4
0101 = 5
0110 = 6
0111 = 7
1000 = 8
1001 = 9
1010 = 10

Hope this would help you understand how numbers are generated in binary or any number system :)

Answer 2

Decimal is base 10
Binary is base 2

0 = 0
1 = 1
10 = 2
11 = 3
100 = 4
101 = 5
and so on

Conversion

Heres how you convert 101 from binary to decimal
1*2^2 + 0*2^1 + 1*2^0 = 5

Answer 3

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Answer 4

A quick and comprehensive tutorial on binary numbers is at http://www.math.grin.edu/~rebelsky/Courses/152/97F/Readings/student-binary.html

Answer 5

0000000001001110 0000000001001111 0000000000100001
0000000000100001 0000000000100001