Please answer all questions Consider the following two float

Consider the following two floating point numbers coded in the 10-bit 2. [30 marks] format defined in class: x a 1 1010 01011 0111 01101 and Do the following: (a) carry out the addition, x y, in binary. Show all of the steps of your work, displayed carefully. Make sure your final binary answer is correctly normalized. Convert the result to normalized 10-bit floating point (b) convert both of the numbers, x and y, to decimal form and add the numbers. (c) convert your answer from part (a) to decimal form and compare it with part (b).

Solution

2.

CONVERSION OF HEXA TO DECIMAL

   10 * 16⁷ + 11*16⁶ + 7* 16⁵ + 12 * 16⁴ + 15* 16³+ 0*16² + 0*16¹ +0*16⁰ = 2877091840

DECIMAL VALUE = 2877091840

(A) 1010 1011 0111 1100 1111 0000 0000 0000

(B) 0101 0100 1000 0011 0001 0000 0000 0000

(C )      MSB BIT IS SIGNED BIT      0- POSITIVE , 1-NEGATINE

         SMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM

                 S-SIGN ,M-MAGNITUDE

     

         0 101 0100 1000 0011 0001 0000 0000 0000

(d. )SIGN * 2^EXPONENT * MANTISSA

        BINARY :   S   EEEEEEEE MMMMMMMMMMMMMMMMMMMMMM

           0 10011110   01010110111110011110000