Mitsubishi Digital Electronics FX2N Manual

A SERVICE OF

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FX Series Programmable Controllers Devices in Detail 4

4-48

4.15.2 Floating Point Format

Floatin

g

point format extends the abilities and ran

g

es provided b

y

Scientific Notation with the

abilit

y

to represent fractional portions of whole numbers, for example;

Performin

g

and displa

y

in

g

the calculation of 22 divided b

y

7 would

y

ield the followin

g

results:

a) Normal FX operation usin

g

decimal (inte

g

ers) numbers would equal 3 remainder 1

b) In floatin

g

point it would equal 3.14285 (approximatel

y

)

c) In Scientific format this calculation would be equal to 3142 10

-3

So it can be seen that a

g

reater de

g

ree of accurac

y

is provided b

y

floatin

g

point numbers, i.e.

throu

g

h the use of lar

g

er numerical ran

g

es and the availabilit

y

of more calculable di

g

its.

Hence, calculations usin

g

floatin

g

point data have some si

g

nificant advanta

g

es. Decimal data

can be converted in to floatin

g

point b

y

usin

g

the FLT, float instruction (FNC 49). When this

same instruction is used with the float fa

g

M8023 set ON, floatin

g

point numbers can be

converted back to decimal. see pa

g

e 5-49 for more details.

The followin

g

points should be remembered about the use of Floatin

g

Point within appropriate

FX units;

• Floatin

g

point numbers, no matter what numerical value, will alwa

y

s occup

y

two consecu-

tive data re

g

isters (or 32 bits).

• Floatin

g

point values cannot be directl

y

monitored, as the

y

are stored in a special format

recommended b

y

the I.E.E.E (Institute of Electrical and Electronic En

g

ineers) for personal

and micro computer applications.

• Floatin

g

point numbers have both mantissa and exponents (see Scientific Notation for an

explanation of these terms). In the case of floatin

g

point exponents, onl

y

8 bits are used.

Additionall

y

there is a sin

g

le si

g

n bit

for the mantissa. The remainin

g

bits

of the 32 bit value, i.e. 23 bits, are

used to ‘describe’ the mantissa

value.

Valid ran

g

es for floatin

g

point numbers as used in FX Main Processin

g

Units:

Description Sign

Exponent

(bit pattern)

Mantissa

(bit pattern)

Remark

Normal Float

0 or 1

11111110

00000001

11111111111111111111111

11111111111111111111110

00000000000000000000001

00000000000000000000000

Lar

g

est number +/- 3.403 10

38

Accurac

y

: 7 si

g

nificant fi

g

ures

Smallest number +/- 1.175

10

-38

Zero

0 or 1

00000000 00000000000000000000000 All di

g

its are 0 (zero)

b15 b0

Data re

g

ister 'D+1'

(16 bits)

b15 b0

Data re

g

ister 'D'

(16 bits)

Si

g

n bit

Exponet

(8 bits)

Mantissa

(23 bits)

FX Data Re

g

ister Contruction

Floatin

g

Point Format