PROGRAMMABLE LOGIC CONTROL.(LL)>CUSTOM<
PROGRAMMABLE LOGIC CONTROL.(LL)>CUSTOM<
5th Edition
ISBN: 9781266481475
Author: Petruzella
Publisher: MCG
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Chapter 3, Problem 6RQ
Program Plan Intro

Hexadecimal number system:

  • In hexadecimal number system, the numbers from “0” to “9” and letters from “A” to “F” are used.
  • It means, in total, hexadecimal system has 10 numbers and 6 alphabets.
  • Therefore, the base used for hexadecimal numbering system is 16.

Binary number system:

  • In binary system, the numbers “0” and “1” are only used.
  • It means, in total, binary system has only 2 numbers.
  • Therefore, the base used for binary numbering system is 2.

Explanation of Solution

b.

Conversion of hexadecimal number E8 to its equivalent binary number:

  • Given, hexadecimal number is E8.
  • Each digit of the hexadecimal number is converted into four bit binary equivalent.
  • A group of four bit binary refers to its corresponding hexadecimal digit.
  • Finally, the binary notation of the given hexadecimal number is noted.
  • The following diagram describes the binary notation of the hexadecimal number E8...

Explanation of Solution

c.

Conversion of hexadecimal number 6D2 to its equivalent binary number:

  • Given, hexadecimal number is 6D2.
  • Each digit of the hexadecimal number is converted into four bit binary equivalent.
  • A group of four bit binary refers to its corresponding hexadecimal digit.
  • Finally, the binary notation of the given hexadecimal number is noted.
  • The following diagram describes the binary notation of the hexadecimal number 6D2.

Explanation of Solution

d.

Conversion of hexadecimal number 31B to its equivalent binary number:

  • Given, hexadecimal number is 31B.
  • Each digit of the hexadecimal number is converted into four bit binary equivalent.
  • A group of four bit binary refers to its corresponding hexadecimal digit.
  • Finally, the binary notation of the given hexadecimal number is noted.
  • The following diagram describes the binary notation of the hexadecimal number 31B.

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1.) Consider the problem of determining whether a DFA and a regular expression are equivalent. Express this problem as a language and show that it is decidable. ii) Let ALLDFA = {(A)| A is a DFA and L(A) = "}. Show that ALLDFA is decidable. iii) Let AECFG = {(G)| G is a CFG that generates &}. Show that AECFG is decidable. iv) Let ETM {(M)| M is a TM and L(M) = 0}. Show that ETM, the complement of Erm, is Turing-recognizable. Let X be the set {1, 2, 3, 4, 5} and Y be the set {6, 7, 8, 9, 10). We describe the functions f: XY and g: XY in the following tables. Answer each part and give a reason for each negative answer. n f(n) n g(n) 1 6 1 10 2 7 2 9 3 6 3 8 4 7 4 7 5 6 5 6 Aa. Is f one-to-one? b. Is fonto? c. Is fa correspondence? Ad. Is g one-to-one? e. Is g onto? f. Is g a correspondence? vi) Let B be the set of all infinite sequences over {0,1}. Show that B is uncountable using a proof by diagonalization.
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