Introduction to Industrial Automation

Figure A.1  Decimal number system.

Binary number

Position value

Position value as

power of 2

Multiplication of binary

digit and position value

Decimal number

1 1 1

1 1 1 1

0

2

10

128

64

32

16

8

4

2

1

128

64

32

16

8

4

2

1

2

7

2

6

2

5

2

4

2

3

2

2

2

1

2

0

+

239

Figure A.2  Binary system of numbers and their conversion to the decimal system.

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Appendix A 

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411

a binary number with the lowest position value is called the “least significant bit” or LSB, while 

the digit with the highest position value is called the “most significant bit” or MSB. In order to 

convert a decimal number to a binary one, the procedure illustrated i

means dividing successively the decimal number by 2 and denoting the remainders 0 or 1 as digits 

of the binary number.