1 Let r 12 12 in decimal 11 How is r represented in the IEEE

1. Let r 12 12 (in decimal) 1.1 How is r represented in the IEEE floating point standard in double precision (i.e., a total of 8 bytes)? 1.2 In single precision 1.e. using a total of 4 bytes), what are the two nearest machine numbers to ar? 1.3 In single precision, what are the precise relative errors of the two nearest machine numbers?

Solution

1.1) the double precision floating point representation of the value 4096.00024 is

4096.0002400000003035529516637325286865234375

1.2) the nearest value in single precision for the given value 4096.00024 is 4096.

1.3) minimum rounding value:0.0000000595999 and maximum rounding value:0.000000118999