Decimal to Binary

Input : any Decimal Number

Output : Binary format 

Logic:

1) Take any natural number say..10.

2)  divide by 2, and find remainder...repeat the same process until u get 0.

divisor number remainder

         2 10 (0)

          ---------------------------------

      2 5 (1)

      ----------------------------------

      2 2 (0)

      ----------------------------------

      2 1 (1)

      ----------------------------------

            0

3) Now look at the remainder pattern from bottom to top, ie. 1010 which is an equivallent for decimal number 10.

Combination of Strings

Input : Any number of Strings

Output : Combinations of Strings

for eg: A,B,C(input)

then Output : 

A

B

C

AB
AC

AD

BC

BD

CD

ABC

mathematical formula : nCr =  n ! / (n-r) ! r !

Algorithm with explanations:

1) Enter the number of strings.

          Let say 3. A,B and C.

2) now loop from i=1 to 2^3-1 = 7 (in general (2^n) -1 ).

3) Observe binary patterns for each of the numbers coming in that loop.

     like in the following case.

Number Bianry Pattern

(A) (B) (C)

  1 0 0 1

2 0 1 0

3 0 1 1

4 1 0 0

5 1 0 1

6 1 1 0

7 1 1 1       

4) now put the appropriate string where 1 appears, and put nothing in case of 0.

ie.

1st entry becomes C

2nd entry B

3 BC

4 A

5 AC

6 AB

7 ABC

Thats all  u need.

Thanks