How to Check Sum ?

 I have confusion in Checksum calculation for the Data 10101001 Data1 00111001 Data2 ---------- 11100010 SUM How this Sum get calculated, you done the binary sum or what is real method as If I do 1+0 you are showing 1, for 1+1 also 1 but at the last element 1+1 it is shown as zero why?

Binary addition works on the same principle, but the numerals are different. Begin with one-bit binary addition:

    0    0    1
   +0   +1   +0
  ___  ___  ___
    0    1    1
1+1 carries us into the next column. In decimal form, 1+1=2.In binary, any digit higher than 1 puts us a column to the left (as would 10 in decimal notation).The decimal number "2" is written in binary notation as "10". Record the 0 in the ones column, and carry the 1 to the twos column to get an answer of "10." In our vertical notation,

    1
   +1
  ___
   10
The process is the same for multiple-bit binary numbers:
         1010
        +1111
       ______
Step one:
Column 1(from right) :0+1=1.
Record the 1.
Temporary Result: 1; Carry: 0
Step two:
Column 2(from right): 1+1=10.
Record the 0, carry the 1.
Temporary Result: 01; Carry: 1
Step three:
Column 3(from right): 1+0=1 Add 1 from carry: 1+1=10.
Record the 0, carry the 1.
Temporary Result: 001; Carry: 1
Step four:
Column 4(from right): 1+1=10. Add 1 from carry: 10+1=11.
Record the 11.
Final result: 11001
Hope it would now be clear to you.