Computer Organization and Embedded Systems (6th Edition)

Chapter 9, Arithmetic problem 22P

D]Consider a 16-bit, oating-point number in a format similar to that discussed in Problem 9.21, with a 6-bit exponent and a 9-bit mantissa fraction. The base of the scale factor is 2 and the exponent is represented in excess-31 format. (a) Add the numbers Aand B, formatted as follows: A= B= 0 100001 111111110 0 011111 001010101 Give the answer in normalized form. Remember that an implicit 1 is to the left of the binary point but is not included in the Aand Bformats. Use rounding as the truncation method when producing the nal mantissa. (b) Using decimal numbers w,x,y, and z, express the magnitude of the largest and smallest (nonzero) values representable in the preceding normalized oating-point format. Use the following form: Largest = w 2x Smallest = y 2z

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