Introduction to Industrial Automation

A.3.1   Negative  Numbers

The CPU of various PLCs process the analog values in a binary form only. Analog input modules 

convert the analog process signal into digital form, and analog output modules convert the digital 

output value into an analog signal. The representation of a digitized analog value depends on the 

number of used bits (resolution), which has to include both positive and negative numbers. In the 

decimal arithmetic system, negative or positive numbers are denoted with a minus or plus sign 

in front of them, which means that each number has two parts: the sign that is a symbol and the 

magnitude. Therefore, this method of digitized value representation is not applicable in a digital 

device like the PLC.

The simplest method to represent a negative number as a binary number is to use an extra digit, 

called a “sign bit”, which usually is the fifteenth bit (MSB) for a 16-bit resolution. If the sign bit is 

0 (1), this means that the number is positive (negative), such as the signed binary numbers shown 

i
A second method for the representation of negative numbers in a digital device is to use 

the complement of a binary number, and particularly the one’s complement or two’s comple-

ment. When a binary number, has the value 1 the complement is 0 and vice versa, that is called 

the one’s complement. For example, the one’s complement of the binary number 0110 is 1001. 

Binary number

Decimal number

1 1 1

1 1 1 1

2

0

10

239

119 Remainder

1

59

Remainder

1

29

Remainder

1

14

Remainder

1

7

Remainder

0

3

Remainder

1

1

0

Remainder

1

Remainder

1

2

119

2

59

2

29

2

14

2

7

2

3

2

1

2