5 Categories & Use of Application Instructions Binary Floating Point DVP-PLC represents floating points in 32 bits, following the IEEE754 standard: b 31 b 0 0: positive 1: negative ( ) M B E S .1 2 1 Ч Ч − − , in which B = 127 Sign bit Therefore, the range for the 32-bit floating point is ±2 -126 ~ ±2 +128 , i.e. ±1.1755 Ч 10 -38 ~ ±3.4028 Ч 10 +38 Example 1: Representing "23" in 32-bit floating point Step 1: Convert “23” into a binary value: 23.0 = 10111 Step 2: Normalize the binary value: 10111 = 1.0111 Ч 2 4 , in which 0111 is mantissa and 4 is exponent Step 3: Obtain the exponent: ∵ E – B = 4 E – 127 = 4 ∴ E = 131 = 10000011 2 Step 4:
Combine the sign bit, exponent and mantissa into a floating point 0 100 0001 1 011 1000 0000 0000 0000 0000 2 = 41B80000 16 Example 2: Representing “-23.0” in 32-bit floating point The steps required are the same as those in Example 1. The only difference is you have to alter the sign bit into “1”. DVP-PLC uses registers of 2 continuous No. to combine into a 32-bit floating point. For example, we use registers (D1, D0) for storing a binary floating point as below: D1(b15~b0) D0(b15~b0) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 7 6 5 1 0 -1 -2 -3 -17 -18 -19 -20 -21 -22 -23 b0 b1 b2 b3 b4 b5 b6 b20 b21 b22 b23 b24 b28 b29 b30 b31 8 bits of exponent 23 bits of mantissa Hidden decimal point Sign bit (0:
positive 1: negative) When b0~b31 is 0, the content is 0. Decimal Floating Point Since the binary floating point are not very user-friendly, we can convert it into a decimal floating point for use. Please be noted that the decimal point operation in DVP-PLC is still in binary floating point. The decimal floating point is represented by 2 continuous registers. The register of smaller No. is for the constant while the register of bigger No. is for the exponent. Example:
Storing a decimal floating point in registers (D1, D0) Decimal floating point = [constant D0] Ч 10 [exponent D1 ] Constant D0 = ±1,000 ~ ±9,999 Exponent D1 = -41 ~ +35 The constant 100 does not exist in D0 due to 100 is represented as 1,000 Ч 10 -1 . The range of decimal floating point DVP-PLC Application Manual 5-13 8 bits S exponent mantissa S E7 E6 E5 E1 E0 A22 A21 A20 A6 A5 A4 A3 A2 A1 A0 Hidden de