Question

1. Show how the following decimal numbers are stored in 6-bit 2's complement format. Explain any discrepancies. (a) -32 (b) 25 (c) 32 (3 Marks)

Answer 1

Theory: A 6 bit 2's complement form can be used to represent the numbers from-32 to 31 To find 2's complement of a negative number find the complement of the positive equivalent of that number and then add 1 to it. .To convert a positive number to its 2's complement form just represent it in binary format (a) 32 32-100000 Thus -32 in 6 bit 2's complement form is 100000 (b) 25 . Since it is positive number 2's complement is number itself with MSB as 0 .Thus 2's complement 011001 Thus 25 in 6 bit 2's complement form is 011001 (c) 32 AS we mentioned in above theory part maximum number that can be represented using 6 bit 2's complement form is 31. . Thus 32 is incompatible with 6 bit 2's complement form Thus 32 is a discrepancy or incompatible here.