For each machine-representable number r, define f (r) to be the next larger machine- representable number. Consider the following statements: (a) For fixed-point (integer) arithmetic, the distance between r and f (r) is constant. (b) For floating-point arithmetic, the relative distance | (f(r)-r) /r | is con- stant (for r # 0). Are the statements true or false? Give examples or counterexamples to explain your rea- soning.²

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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For each machine-representable number r, define f (r) to be the next larger machine-
representable number. Consider the following statements:
(a) For fixed-point (integer) arithmetic, the distance between r and f(r) is
constant.
(b) For floating-point arithmetic, the relative distance | (f(r) -r) /r | is con-
stant (for r = 0).
Are the statements true or false? Give examples or counterexamples to explain your rea-
soning.²
2
Transcribed Image Text:For each machine-representable number r, define f (r) to be the next larger machine- representable number. Consider the following statements: (a) For fixed-point (integer) arithmetic, the distance between r and f(r) is constant. (b) For floating-point arithmetic, the relative distance | (f(r) -r) /r | is con- stant (for r = 0). Are the statements true or false? Give examples or counterexamples to explain your rea- soning.² 2
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