Page 76 - Programmable Logic Controllers, Fifth Edition - Mobile version

In the result, if the carry is a 1, then the result is positive;
The process for dividing one binary number by an-
if the carry is a 0, then the result is negative and requires other is the same for both binary and decimal numbers, as
a minus sign. shown in the following example.
Decimal Equivalent binary
EXAMPLE 10-4 7 111
_
_
2 q14 10q1110
Subtract 101 from 111.
10
111 11
+ − 011 The 2’s complement 10
1010 The first 1 indicates that 10
the result is positive, so it 10
is disregarded: 00
010 The basic function of a comparator is to compare the
relative magnitude of two quantities. PLC data compari-
son instructions are used to compare the data stored in
two words (or registers). At times, devices may need to
EXAMPLE 10-5 be controlled when they are less than, equal to, or greater
than other data values or set points used in the applica-
Subtract 11011 from 01101.
tion, such as timer and counter values. The basic compare
01101 instructions are as follows:
+ − 00101 The 2’s complement A = B (A equals B)
10010 There is no carry, so the result is A > B (A is greater than B)
negative; therefore a 1 has to be
subtracted and the 1’s complement A < B (A is less than B)
taken to give the result: 3.11 Floating Point Arithmetic
subtract 1 10010 − 1 = 10001
1’s complement −01110 Certain PLC-related computations are performed using
floating point arithmetic. The term floating point refers
to the fact that the decimal point can float or be placed
anywhere relative to the significant digits of the number.
Binary numbers are multiplied in the same manner The main features of floating-point representation are:
as decimal numbers. When multiplying binary numbers,
there are only four conditions that can occur: • Floating point can support a much wider range of
values. It can represent numbers that are very small
0 × 0 = 0 or numbers that are very large.
0 × 1 = 0 • Floating point provides an easy method of dealing
1 × 0 = 0 with fractions. Without floating point, a PLC word
1 × 1 = 1 can only represent an integer or whole number.
An example of a floating point number system is shown
To multiply numbers with more than one digit, form in Figure 3-16. The representations shown in this example
partial products and add them together, as shown in the
following example.
Floating point representation of 4,234
Decimal Equivalent binary 423,400.0 × 10 –2
42,340.0 × 10 –1
5 101 4,234.0 × 10
×6 ×110 423.4 × 10 1
30 000 42.34 × 10 2
101 4.234 × 10 3
101 0.4234 × 10 4
11110 Figure 3-16 Example of a floating point number system.

Number Systems and Codes Chapter 3 57

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