1's and 2's Complement

1's Complement: The 1's complement of a binary number is obtained by changing each 0 to a 1 and each 1 ta a 0, In other words, change each bit in the number to its complement. The process is shown below.

                         Find 1's Complement of 101011?
                                    Answer: 1-0
                                                0-1
                                                1-0
                                                0-1
                                                1-0
                                                1-0
                                                1-0

2's Complement: The 2's complement of a binary number is formed by taking the 1's complement of the number and adding 1 to the least significant bit position. The process is illustrated below.

                                Find 2's Complement of 101001?
                                                101001    
                                           +   010110
                                 Answer:    010111           

Boolean Algebra:  A division of mathematics which deals with operations on logical values. Boolean algebra traces its origins to an 1854 book by mathematician George Boole. The distinguishing factor of Boolean algebra is that it deals only with the study of binary variables. Most commonly Boolean variables are presented with the possible values of 1 ("true") or 0 ("false"). Variables can also have more complex interpretations, such as in set theory.