b) (i)Is it possible to design a 3-bit binary code to represent each of the 7 digits of the base-7 number system that is also self-complementing? How, if it is possible, and why not, if it is not possible? (ii)Is it possible to design a 3-bit binary code to represent each of the 8 digits of the base-8 number system that is also self-complementing? How, if it is possible, and why not, if it is not possible? [Remember: a code is self-complementing when the complementary digits in base 7 encode into complementary triplets in the 3-bit representation; for instance BCD is not self-complementing, for 0 and 9 are complementing, but 0000 and 1001 are not; the 2421 code is self-complementing]

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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b) (i)Is it possible to design a 3-bit binary code to represent each of the 7
digits of the base-7 number system that is also self-complementing? How, if
it is possible, and why not, if it is not possible? (ii)Is it possible to design a
3-bit binary code to represent each of the 8 digits of the base-8 number
system that is also self-complementing? How, if it is possible, and why not,
if it is not possible? [Remember: a code is self-complementing when the
complementary digits in base 7 encode into complementary triplets in the
3-bit representation; for instance BCD is not self-complementing, for 0 and
9 are complementing, but 0000 and 1001 are not; the 2421 code is
self-complementing]
Transcribed Image Text:b) (i)Is it possible to design a 3-bit binary code to represent each of the 7 digits of the base-7 number system that is also self-complementing? How, if it is possible, and why not, if it is not possible? (ii)Is it possible to design a 3-bit binary code to represent each of the 8 digits of the base-8 number system that is also self-complementing? How, if it is possible, and why not, if it is not possible? [Remember: a code is self-complementing when the complementary digits in base 7 encode into complementary triplets in the 3-bit representation; for instance BCD is not self-complementing, for 0 and 9 are complementing, but 0000 and 1001 are not; the 2421 code is self-complementing]
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