Programmable Logic Controllers
Programmable Logic Controllers
5th Edition
ISBN: 9780073373843
Author: Frank D. Petruzella
Publisher: McGraw-Hill Education
Expert Solution & Answer
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Chapter 3, Problem 1RQ

a.

Explanation of Solution

Conversion of binary numbers to decimal numbers:

  • Given, binary number is 10.
  • First, multiply the given binary number 10 with multiples of 2, with respect to their positions and then, add all the values to get the final answer.
  • The following calculation describes the decimal notation of the binary number 10.

10=21*1+20*0 =2*1+1*0 =2+0 =2

  • Therefore, the decimal notation of binary number (10)2 is “(2)10”.

b.

Explanation of Solution

Conversion of binary numbers to decimal numbers:

  • Given, binary number is 100.
  • First, multiply the given binary number 100 with multiples of 2, with respect to their positions and then, add all the values to get the final answer.
  • The following calculation describes the decimal notation of the binary number 100.

100=22*1+21*0+20*0 =4*1+2*0+1*0 =4+0+0 =4

  • Therefore, the decimal notation of binary number (100)2 is “(4)10”.

c.

Explanation of Solution

Conversion of binary numbers to decimal numbers:

  • Given, binary number is 111.
  • First, multiply the given binary number 111 with multiples of 2, with respect to their positions and then, add all the values to get the final answer.
  • The following calculation describes the decimal notation of the binary number 111.

111=22*1+21*1+20*1 =4*1+2*1+1*1 =4+2+1 =7

  • Therefore, the decimal notation of binary number (111)2 is “(7)10”.

d.

Explanation of Solution

Conversion of binary numbers to decimal numbers:

  • Given, binary number is 1011.
  • First, multiply the given binary number 1011 with multiples of 2, with respect to their positions and then, add all the values to get the final answer.
  • The following calculation describes the decimal notation of the binary number 1011.

1011=23*1+22*0+21*1+20*1 =8*1+4*0+2*1+1*1 =8+0+2+1 =11

  • Therefore, the decimal notation of binary number (1011)2 is “(11)10”.

e.

Explanation of Solution

Conversion of binary numbers to decimal numbers:

  • Given, binary number is 1100.
  • First, multiply the given binary number 1100 with multiples of 2, with respect to their positions and then, add all the values to get the final answer.
  • The following calculation describes the decimal notation of the binary number 1100.

1100=23*1+22*1+21*0+20*0 =8*1+4*1+2*0+1*0 =8+4+0+0 =12

  • Therefore, the decimal notation of binary number (1100)2  is “(12)10”.

f.

Explanation of Solution

Conversion of binary numbers to decimal numbers:

  • Given, binary number is 10010.
  • First, multiply the given binary number 10010 with multiples of 2, with respect to their positions and then, add all the values to get the final answer.
  • The following calculation describes the decimal notation of the binary number 10010.

10010=24*1+23*0+22*0+21*1+20*0 =16*1+8*0+4*0+2*1+1*0 =16+0+0+2+0 =18

  • Therefore, the decimal notation of binary number (10010)2 is “(18)10”.

g.

Explanation of Solution

Conversion of binary numbers to decimal numbers:

  • Given, binary number is 10101.
  • First, multiply the given binary number 10101 with multiples of 2, with respect to their positions and then, add all the values to get the final answer.
  • The following calculation describes the decimal notation of the binary number 10101.

10101=24*1+23*0+22*1+21*0+20*1 =16*1+8*0+4*1+2*0+1*1 =16+0+4+0+1 =21

  • Therefore, the decimal notation of binary number (10101)2 is “(21)10”.

h.

Explanation of Solution

Conversion of binary numbers to decimal numbers:

  • Given, binary number is 11111.
  • First, multiply the given binary number 11111 with multiples of 2, with respect to their positions and then, add all the values to get the final answer.
  • The following calculation describes the decimal notation of the binary number 11111.

11111=24*1+23*1+22*1+21*1+20*1 =16*1+8*1+4*1+2*1+1*1 =16+8+4+2+1 =31

  • Therefore, the decimal notation of binary number (11111)2 is “(31)10”.

h.

Explanation of Solution

Conversion of binary numbers to decimal numbers:

  • Given, binary number is 11001101.
  • First, multiply the given binary number 11001101 with multiples of 2, with respect to their positions and then, add all the values to get the final answer.
  • The following calculation describes the decimal notation of the binary number 11001101.

11001101=27*1+26*1+25*0+24*0+23*1+22*1+21*0+20*1 =128*1+64*1+32*0+16*0+8*1+4*1+2*0+1*1 =128+64+0+0+8+4+0+1 =205

  • Therefore, the decimal notation of binary number (11001101)2 is “(205)10”.

j.

Explanation of Solution

Conversion of binary numbers to decimal numbers:

  • Given, binary number is 11100011.
  • First, multiply the given binary number 11100011 with multiples of 2, with respect to their positions and then, add all the values to get the final answer.
  • The following calculation describes the decimal notation of the binary number 11100011.

11100011=27*1+26*1+25*1+24*0+23*0+22*0+21*1+20*1 =128*1+64*1+32*1+16*0+8*0+4*0+2*1+1*1 =128+64+32+0+0+0+2+1 =227

  • Therefore, the decimal notation of binary number (11100011)2 is “(227)10”.

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