Question

Assume that a mad scientist has created a computer that has 9 bit registers. The most significant bit is the sign bit. He wants to execute the following operation using 9 bit register. -256 - 2 Use 2's complement method (in binary) to find the result of the above operation in binary system. Show the computations in the answer. a Formar CB I U A Addit Record Audio

Answer 1

256 = 100000000 (Cannot be stored in a 9-bit signed variable)

-256 = 011111111 + 1 = 100000000 (Can be stored in a 9-bit signed variable & this is also the smallest value that can be stored)

2 = 000000010

we know that A - B = A + (B' + 1)   in 2's Complement method

so ANS = 100000000 + (000000010' + 1)

             = 100000000 + (111111101 + 1) = 100000000 + 111111110

             = 1 011111110

The last carry over bit being 1 signifies that the result of the operation is negative and has also gone out of bounds of the limit of a 9-bit register to store the data, thereby resulting in an error or otherwise an incorrect result as +254.