Question

6. The exponent in IEEE format floating point numbers are not represented in 2's complement format. Why not? What number is indicated if the value stored in the exponent is zero? What exponent and fraction are used to represent "not-a-number"? 7. This question deals with two numbers in IEEE format (A - 0x3F400000, B 0x3DB00000 (a) Calculate A+B using the floating-point addition procedure discussed in class. Determine the single precision result and express your answer in IEEE floating-point format. Convert your result to decimal and show all steps involved, (b) Calculate A*B using the floating-point addition procedure discussed in class. Determine the single precision result and express your answer in IEEE floating-point format. Convert your result to decimal and show all steps involved,

Answer 1

6). In integers, by using 2's complement for negative numbers makes the arithmetic ``easy;'' we can add two numbers together without thinking about whether number is positive or negative, and get the right answer. This won't work for floating point numbers because the exponents need to be manipulated; if we are using a 2's complement representation for the entire word we'd have to reconstruct the exponent any time we wanted to add or subtract, so it wouldn't gain us anything; in fact, trying to do arithmetic involving a negative number would involve converting it to positive first.

The exponent = 0 can be used to represent the smallest number.

To represent NaN (Not a number) : if all bits of exponent are 1, and any of the matissa bits are 1