Floating-Point Numbers - Delta AS Series Operation Manual

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5.2.2 Floating-point Numbers

The floating-point numbers are represented by decimal points in ISPSoft / DIADesigner. For example, the
floating-point number of 500 is 500.0. Refer to Section 2.2.2 in the AS Series Programming Manual for more
information.
5.2.2.1 Single-precision Floating-point Numbers
Floating-point numbers are represented by the 32-bit register. The representation adopts the IEEE754 standard,
and the format is as follows.
S
b
31
Equation:
The single-precision floating-point numbers range from ±2-126 to ±2+128, and correspond to the range from
±1.1755×10-38 to ±3.4028×10+38.
The AS series PLC uses two consecutive registers to form a 32-bit floating-point number. Take (D1, D0) for
example.
S E7
b31 b30
Example 1:
23 is represented by a single-precision floating-point number.
Step 1: Convert 23 into the binary number, i.e. 23.0=10111.
Step 2: Normalize the binary number, i.e. 10111=1.0111 ×24 (0111 is the mantissa, and 4 is the exponent.).
Step 3: Get the value of the exponent.
Step 4: Combine the sign bit, the exponent, and the mantissa to form the floating-point number.
8 -b it
E xpo ne nt
S ig n b it
0 : Po siti ve
1 : Neg ati ve
( )
S
E B
− 1 × 2 − × . 1 M ; B
D1 (b 15 ~b 0)
2 2 2 2 2
E6 E5 E1 E0 A22 A21 A20
b29 b28 b24 b23
E xp on en t ( 8 b its )
Ma nt iss a s ign b it (0 : Po s it iv e; 1: Ne ga tiv e)
W hen b 0~ b3 1 a re z eros , t he c on te nt is z ero .
∵ E-B=4→E-127=4 ∴ E=131=100000112
0 10000011 01110000000000000000000
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2 3- bi t
Ma nti ssa
b
0
= 127
D0 (b 15 ~b 0)
2 2 2 2 2
A6 A5
b22 b21 b20 b6 b5
Ma nt iss a (2 3b it s )
T he pos ition w here the d eci mal point is hid den
=41B80000
2 16
2 2 2 2 2
A4 A3 A2 A1 A0
b4 b3 b2 b1 b0