Question

Consider the number below, which is stored inside a computer which uses 16-bit 2’s complement base 2 representation. 1101011001110101

(a) Is this number negative? Why, or why not?

(b) Show the resulting value (“bit pattern”) after apply the 2’s complement negation operation to the given value. Is the resulting 2’s complement value (“bit pattern”) a negative number? Explain your answer.

Answer 1

(a) The given number 1101011001110101 is a negetive number. The leftmost bit in a binary number denotes the sign bit. If it is 1 the no. is negetive otherwise positive.

(b) To find the 2's complement of the given no. 1101011001110101 , we need to first find it's 1's complement.

• One's complement of 1101011001110101 = 0010100110001010
• Two's complement of  0010100110001011 = adding 1 to 1's complement obtained above.

=  0010100110001010 + 1 = 0010100110001011

Therefore 2's compliment =  0010100110001011 is a positive number since it's leftmost bit is 0.