Consider the following two 9-bit floating-point representations based on the IEE
ID: 3803594 • Letter: C
Question
Consider the following two 9-bit floating-point representations based on the IEEE floating point format. Neither has a sign bit--they can only represent nonnegative numbers. Format A There are k = 4 exponent bits. The exponent bias is 7. There are n = 5 fraction bits. Format B There are k = 5 exponent bits. The exponent bias is 15. There are n = 4 fraction bits. Below, you are given some bit patterns in Format A, and your task is to convert them to the closest value in Format B. If necessary, you should apply the round-to-even rounding rule. in addition, give the values of numbers given by the Format A and Format B bit patterns. Specify values as whole numbers or decimals. Finally, to summarize the types expected for blanks----Please enter a numeric value for the Value field and enter either a 1 or a 0 for each box in the Bits field.Explanation / Answer
Steps to convert Binary floating point to Deimal:
Example: (Sl No.1) has been illustarted below:
Given 011100000 in Format A.
Sign is positive (Given)
Exponent Value:Take least significant 4 bits which is 0000.Hence value is 0.
Mantissa:Most significant 5 digits: 0.001110
Start at the centre and label each number to the left 1,2,4,8,16 and so on. The each number on the right 1/2, 1/4, 1/8 and so on.
Hence (0*1/2)+ (1*1/4)+(1*1/8)+(1*1/16)+(0*1/32) =7/16 =0.4375
Steps to conver decimal into binary floating point.
Convert 0.4375 to equivalent Format B
Binary equivalent is 011100000
Move 6 places to the left to get it normalised. 0.11100000
Exponent bits in format B is 5.
So 0.11100000 | 11111
Sl.No Format A Value Equivalent Format B 1 011100000 0.4375 0.11100000 | 11111 2 101110101 5.75 0.101110101 | 01010 3 110010110 50.0 0.110010110 | 01001