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2b, such that (0.bb.bp)2 is the best approximation to r using p binary places. Method: Initialise: j1, b1, b2,, bp 0 Loop: if jp+ 1 stop. jj+1 If ≥1 [b, 1, -1] Repeat loop (a) Verify that the algorithm converts to 0.11010,

2b, such that (0.bb.bp)2 is the best approximation to r using p binary places. Method: Initialise: j1, b1, b2,, bp 0 Loop: if jp+ 1 stop. jj+1 If ≥1 [b, 1, -1] Repeat loop (a) Verify that the algorithm converts to 0.11010,

Database System Concepts
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
Section: Chapter Questions
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Question 4#

Read the following algorithm:

Algorithm for converting a fraction r into binary with p binary places. Inputs: fraction EQ, 0 < x <1 and number of places pЄN.

Outputs: bits b1, b2b, such that (0.bb.bp)2 is the best approximation to r using p binary places.

Method:

Initialise: j1, b1, b2,, bp 0 Loop: if jp+ 1 stop. jj+1 If ≥1 [b, 1, -1]

Repeat loop

(a) Verify that the algorithm converts to 0.11010, when p= 5. Can you spot how to express exactly in repeating binary?

(b) Express 0.8510 as accurately as possible with 8 binary places. 

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