Question

Let x be a positive real number. Assume that in the left-justified binary representation of x, b53 = 1 and b54 = b55 = b56 = . . . = 0. If xl is the floating-point result from rounding x down and xr is the floating-point result from rounding x up, show that |x - xl| = |x - xr|.

Name: let x be a positive real number assume that in the left justified binary representation of x b53 1 and b54 b55 b56 0 if xl is the floating point result from rounding x down and xr is the flo 36189
Uploaded: 2023-09-24T20:33:57-08:00
Duration: 3 min 28 s
Channel: Sri K
Description: let x be a positive real number assume that in the left justified binary representation of x b53 1 and b54 b55 b56 0 if xl is the floating point result from rounding x down and xr is the flo 36189

          Let x be a positive real number. Assume that in the left-justified binary representation of x, b53 = 1 and b54 = b55 = b56 = . . . = 0. If xl is the floating-point result from rounding x down and xr is the floating-point result from rounding x up, show that |x - xl| = |x - xr|.

Added by Frank R.

Computer Science and Information Technology

Trishna Knowledge Systems 2018 Edition

Instant Answer

Solved by Expert Sri K

09/24/2023

Step 1

.. = 0. This means that x lies between 2^53 and 2^54 in binary representation. Show more…

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Let x be a positive real number. Assume that in the left-justified binary representation of x, b53 = 1 and b54 = b55 = b56 = . . . = 0. If xl is the floating-point result from rounding x down and xr is the floating-point result from rounding x up, show that |x - xl| = |x - xr|.