1 Numeric Values Handled in PLC (Octal, Decimal, Hexadecimal and Real Numbers)

FX3S/FX3G/FX3GC/FX3U/FX3UC Series

Programming Manual - Basic & Applied Instruction Edition



5.1.2



5 How to Specify Devices and Constants to Instructions

5.1 Numeric Values Handled in PLC (Octal, Decimal, Hexadecimal and Real Numbers)



Conversion of numeric values

Numeric values handled in FX PLCs can be converted as shown in the table below:

Decimal number (DEC)



Octal number (OCT)



Hexadecimal number

(HEX)



0



0



00



0000



0000



0000



0000



1



1



01



0000



0001



0000



0001



2



2



02



0000



0010



0000



0010



3



3



03



0000



0011



0000



0011



4



4



04



0000



0100



0000



0100



5



5



05



0000



0101



0000



0101



6



6



06



0000



0110



0000



0110



7



7



07



0000



0111



0000



0111



8



10



08



0000



1000



0000



1000



0B



0000



1011



0001



0001



12



14



0C



0000



1100



0001



0010



13



15



0D



0000



1101



0001



0011



14



16



0E



0000



1110



0001



0100



15



17



0F



0000



1111



0001



0101



16



20



10



0001



0000



0001



0110



99



143



0011



1001



1001



Octal number (OCT)



Hexadecimal number

(HEX)



•••



0110



•••



63



•••



•••



13



•••



0000



11



•••



1001



•••



0000

0001



•••



1001

1010



•••



0000

0000



•••



09

0A



•••



11

12



•••



9

10



•••



BCD



•••



Binary number (BIN)



Major applications

Decimal number (DEC)

Constants (K) and

numbers of internal

devices except I/O

relays



154



Numbers of internal

I/O relays



Constants (H)



Binary number (BIN)

Processing inside

PLC



BCD

BCD digital switches

and seven-segment

display units



FX3S/FX3G/FX3GC/FX3U/FX3UC Series



5 How to Specify Devices and Constants to Instructions



Programming Manual - Basic & Applied Instruction Edition



1



Handling of numeric values in floating point operations



Introduction



5.1.3



5.1 Numeric Values Handled in PLC (Octal, Decimal, Hexadecimal and Real Numbers)



3



When handling a binary floating point (real number) in data registers, use a pair of data registers having consecutive

device numbers.

When D11 and D10 are used, for example, a binary floating point is handled as shown below:

D 11(b15 to b0)

2



2



6



2



5



2



1



2



0



D 10(b15 to b0)

2



-1



2



-2



2



-3



2-21



2-22



4



2-23



E7



E6



E5



E1



E0



A22



A21



A20



A2



A1



A0



b31



b30



b29



b28



b24



b23



b22



b21



b20



b2



b1



b0



23 bits in

mantissa part

A0 to A22 = 0 or 1



Sign for mantissa part

(0: Positive, 1: Negative)



0 in case "b0 to b31 = 0"



=



5

Specified the

Device &

Constant



8 bits in

exponent part

E0 to E7 = 0 or 1



Devices

in Detail



S



Binary floating point (real number)



± (20 + A22 × 2−1 + A21 × 2−2 + ... + A0 × 2−23)

× 2 (E7 × 2 + E6 × 2 + ... + E0 × 2 )/2127



Example: A22=1 , A21=0, A20=1, A19 to A0=0, E7=1, E6 to E1=0, E0=1

=

=



± (20 + 1 × 2−1 + 0 × 2−2 + 1 × 2−3 + ... + 0 × 2−23)

× 2 (1 × 2 + 0 × 2 + ... + 1 × 2 )/2127

±1.625 × 2129/2127 = ±1.625 × 22



6

Before

Programming



Binary floating point (real number)



Instruction

List



Binary floating point (real number)



7



2

Overview



Handling of numeric values in floating point operations

Binary integers are handled inside PLCs.

During division of integers, the answer "40 ÷ 3 = 13 ... 1" is obtained, for example.

During square root extraction operations, decimal points are ignored.

In FX3S, FX3G, FX3GC, FX3U and FX3UC PLCs, floating point operations are available to achieve higher accuracy in

such operations.



The sign bit b31 states whether data is positive or negative, but is not handled as a complement.



7

Basic

Instruction



Number of significant figures

The number of significant figures of binary floating point is approximately 7 when expressed in decimal. The binary

floating point range is as follows:

- Least absolute value: 1175494 × 10-44

- Most absolute value: 3402823 × 1032



8



- Zero flag

- Borrow flag

- Carry flag



FNC00-FNC09

Program Flow



Handling of the zero (M8020), borrow (M8021) and carry (M8022) flags

These flags operate as follows in floating point operations.

: 1 when the result is 0

: 1 when the result does not reach the minimum unit but is not 0

: 1 when the absolute value of the result exceeds the available numeric value range.



9

FNC10-FNC19

Move & Compare



Monitoring of binary floating point (real number)

A programming software supporting the display of floating point such as GX Works2 and GX Developer can directly

monitor binary floating point (real number).

A programming tool not supporting the display of floating point can monitor binary floating point (real number) when it

is converted into scientific notation (real number).



10

FNC20-FNC29

Arith. & Logic

Operation



155



FX3S/FX3G/FX3GC/FX3U/FX3UC Series



5 How to Specify Devices and Constants to Instructions



Programming Manual - Basic & Applied Instruction Edition



5.1 Numeric Values Handled in PLC (Octal, Decimal, Hexadecimal and Real Numbers)



Scientific notation (real number)

Because binary floating point (real number) is difficult to understand for users, it can be converted into scientific

notation (real number). But internal operations are executed using binary floating point (real number).

Scientific notation (real number) is handled by a pair of data registers having serial device numbers. Different from

binary floating point (real number), a data register having a smaller device number handles the mantissa part, and the

other data register having a larger device number handles the exponent part.

For example, when data registers D1 and D0 are used, they handle scientific notation as shown below. Data can be

written to D0 and D1 by MOV instruction.

Scientific notation (real number) =



[Mantissa D0] × 10 [Exponent D1]

Mantissa D0 = ± (1000 to 9999) or 0

Exponent D1 = −41 to +35



The most significant bit of D0 and D1 specifies the positive or negative sign respectively, and is handled as the

complement of 2 respectively.

The mantissa D0 does not allow "100", for example. In the case of "100", it is handled as "1000 × 10−1".

The scientific notation (real number) range is as follows:

- Minimum absolute value: 1175 × 10−41

- Maximum absolute value: 3402 × 1035

Number of significant figures

The number of significant figures of scientific notation is approximately 4 when expressed in decimal. The scientific

notation range is as described above.

Scientific notation (real number) is valid in the following instructions:

- Conversion from binary floating point (real number) into scientific notation (real number): FNC118 ([D]EBCD)

- Conversion from scientific notation (real number) into binary floating point (real number): FNC119 ([D]EBIN)



156



FX3S/FX3G/FX3GC/FX3U/FX3UC Series



5 How to Specify Devices and Constants to Instructions



Programming Manual - Basic & Applied Instruction Edition



1



Specification of Constants K, H and E

(Decimal, Hexadecimal and Real Number)



Introduction



5.2



5.2 Specification of Constants K, H and E (Decimal, Hexadecimal and Real Number)



5.2.1



Constant K (decimal number)



- When word data (16 bits) is used ...... K-32768 to K32767

- When double data (32 bits) is used ... K-2,147,483,648 to K2,147,483,647



4



Constant H (hexadecimal number)



Devices

in Detail



"H" indicates a hexadecimal number, and is mainly used to specify numeric values as operands in applied instructions.

(Example: H1234)

When using digits 0 to 9, the bit status (1 or 0) of each bit is equivalent to the BCD code, so BCD data can be specified

also.

(Example: H1234 ... When specifying BCD data, specify each digit of hexadecimal number in 0 to 9.)

The hexadecimal constant setting range is as follows:



5

Specified the

Device &

Constant



- When word data (16 bits) is used ...... H0 to HFFFF

(H0 to H9999 in the case of BCD data)

- When double data (32 bits) is used ... H0 to HFFFFFFFF (H0 to H99999999 in the case of BCD data)



5.2.3



3

Instruction

List



"K" indicates a decimal integer, and is mainly used to specify the set value of timers and counters and numeric values

as operands in applied instructions. (Example: K1234)

The decimal constant specification range is as follows:



5.2.2



2

Overview



When handling constants in a sequence program, use constant K (decimal), H (hexadecimal) or E (floating point).

In peripheral equipment for programming, add "K" to a decimal number, "H" to a hexadecimal number and "E" to a

floating point (real number) for operations associated with numeric values in instructions. (Examples: K100 (decimal

number), H64 (hexadecimal number) and E1.23 (or E1.23 + 10) (real number))

The roles and functions of constants are described below.



Constant E (real number)



6



Specify a numeric value as it is.

For example, specify "10.2345" in the form "E10.2345".



- Exponent expression: ..............



7

Basic

Instruction



- Normal expression: ..................



Before

Programming



"E" indicates a real number (floating point data), and is mainly used to specify numeric values as operands in applied

instructions. (Example: E1.234 or E1.234 + 3)

The real number setting range is from −1.0 × 2128 to −1.0 × 2−126, 0 and 1.0 × 2−126 to 1.0 × 2128.

In a sequence program, a real number can be specified in two methods, "normal expression" and "exponent

expression".



Specify a numeric value in the format "(numeric value) × 10n".

For example, specify "1234" in the form "E1.234 + 3".

"+3" in "E1.234 + 3" indicates "103".



8

FNC00-FNC09

Program Flow



9

FNC10-FNC19

Move & Compare



10

FNC20-FNC29

Arith. & Logic

Operation



157



FX3S/FX3G/FX3GC/FX3U/FX3UC Series



5 How to Specify Devices and Constants to Instructions



Programming Manual - Basic & Applied Instruction Edition



5.3



5.3 Character Strings



Character Strings



Character strings are classified into character string constants which directly specify character strings in operands in

applied instructions and character string data.



5.3.1



Character string constant ("ABC")

A device "character string" directly specifies a character string in a sequence program.

Put half-width characters inside quotation marks (example: "ABCD1234") in specification.

JIS8 code is available.

Up to 32 characters can be specified as a character string.



5.3.2



Character string data

With regard to character string data, a specified device to the NULL code (00H) is handled as one character string in

1-byte units.

When expressing (recognizing) character string data by bit devices with digit specification, however, 16 bits are

required for data including the NULL code (00H) specifying the end of the character string data because the instruction

length is 16 bits. (Refer to Example 2 in the step 2 below.)

In the following cases, an operation error occurs in the applied instruction (error code: K6706):

• When "00H" is not specified in the corresponding device range after the source device number specified in an

applied instruction

• When there are insufficient devices for storing character string data (including "00H" or "0000H" indicating the end

of the character string data) in the destination devices specified in an applied instruction

1)



Character string data stored in word devices

• Example of data which can be

recognized as character string data

b15

D100

D101

D102



b8 b7



• Example of data which cannot be

recognized as character string data



b0



b15



1st character

3rd character

5th character



D100

D101



00H



21st character



D7999 "n"th character



D102



"00H" indicating the end of

the character string can be

detected.



2)



2nd character

4th character

6th character



b0

1st character

3rd character

5th character



…



…

D110



b8 b7



2nd character

4th character

6th character



"(n-1)"th character



"00H" indicating the end of character string

cannot be detected from the specified

device to the end device number.



Character string data stored in bit devices with digit specification

• Example of data which can be

• Examples of data which cannot be

recognized as character string data

recognized as character string data

16 bits

16 bits

M115 to M100 2nd character

M131 to M116 4th character

M147 to M132



00H



13th character



…

M211 to M196



M115 to M100

M131 to M116

M147 to M132



2nd character

4th character

6th character



1st character

3rd character

5th character



…



6th character



1st character

3rd character

5th character



"00H" indicating the

end of the character

string can be

detected.



M7679 to

M7664





M7623 to M7608

M7639 to M7624

M7655 to M7640

M7671 to M7656

M7679 to M7672



"n"th character "(n-1)"th character



"00H" indicating the end of character string

cannot be detected from the specified

device to the end device number.

16 bits

2nd character

4th character

6th character

8th character



1st character

3rd character

5th character

7th character

00H



Because the data "00H" indicating the end

of the character string does not reach 16

bits, the end of the character string cannot

be recognized.



158