Introduction to binary number table:
Binary number system uses 2 as the base just as 10 serves as the base in the decimal system. A number system with base n for any given number n will have a set of n symbols corresponding to numbers from 0 to n-1. Then a two digit number written as ab with base n will have a value equal to

an + b;

where 0 a   n-1 and 0 b   n-1.

Utility of Binary Number System:

Binary number system uses just two symbols 0 and 1 to write all numbers. The two symbols 0 and 1 can easily correspond to two switch positions of on and off. This makes binary number system extremely useful for computer processors. It will be no exaggeration to say that modern day super fast computers could not have been created without use of binary number system.

Numbers with Base 2 in Computers:

Taking the analogy of the general case explained at the beginning to numbers with base 2, we are left with only two symbols 0 and 1. A number written as

arar-1ar-2.......a2a1a0 where 0 ak   1 for every k, will have a value given by the expression

ar*2r + ar-1 *2r-1+ ar-2*2r-2+.......+a2*22 +a1*21 + a0

We can also say that every number can be expressed as a sum of exponents of 2 since all the coefficients in the expressions are either 0 or 1. That is how the processor of your computer understands it and the binary numbers are handled by it in a manner quite different from the way our minds comprehend them.Having problem with Math Questions keep reading my upcoming posts, i will try to help you.

Let us say two numbers 3 and 6 are to be added. Written in binary system they become 011 and 110 respectively. Processor of your computer only knows on and off switches, and it knows that to add off + on and on + off will be on, while off + off and on + on will be off with the added condition that if two on switches are added one more on has to be carried over to next digit on the left.

How the addition goes on inside the processor will be something like what is shown below.

First Number (3)	0 1 1	Off  on  on
Second Number (6)	1 1 0	On  on  off
Result of Addition (3 + 6 = 9 = 23 + 1)	10 0 1	On off  off  on
Notice that on carried over from the second position from the right gives rise to another on being carried over from third position and an additional digit.

Conversion Table for Numbers with Base 2 to Base 10:

Following table can be used to quickly convert numbers with base 3 to decimal system.

Base 2	Base 10	Base 2	Base 10	Base 2	Base 10
0	0	1011	11	10110	22
1	1	1100	12	10111	23
10	2	1101	13	11000	24
11	3	1110	14	11001	25
100	4	1111	15	11010	26
101	5	10000	16	11011	27
110	6	10001	17	11100	28
111	7	10010	18	11101	29
1000	8	10011	19	11110	30
1001	9	10100	20	11111	31
1010	10	10101	21	100000	32

Remembering that in a number system with base 2, 2 will be expressed as 10, 2^2 as 100 and 2^3 as 1000 and in general 2^n as 1 followed by a string of n zeroes will help one identify these landmark points and practice correctly.