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(1 + m) * 2 to the power of (e - bias) = 1.25 * 2 to the power of 3 = 10.If your copy of TIA Portal Step 7 came with USB Memory Stick Floating License, you'll need to move that license to your hard drive before you'll be able to use Step 7. The number 10.0 in the first example results from its floating-point format (hexadecimal representation: 4120 0000) as follows:Į = 2 to the power of 7 + 2 to the power of 1 = 2 + 128 = 130 The following figure shows the floating-point format for the following decimal values: The calculation accuracy of 6 decimal places means, for example, that the addition of number1 + number2 = number1 if number1 is greater than number2 * 10 to the power of y, where y >6:Įxamples of Numbers in Floating-Point Format You can therefore only specify a maximum of 6 decimal places when entering floating-point constants. The floating-point numbers in STEP 7 are accurate to 6 decimal places.
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However, not every bit pattern is a valid number.Īccuracy when Calculating Floating-Point NumbersĬalculations involving a long series of values including very large and very small numbers can produce inaccurate results. If the values for floating-point operations are stored in memory double words, for example, you can modify these values with any bit patterns. You should therefore always evaluate the status bits first in math operations before continuing calculations based on the result. The result "Not a valid floating-point number" is obtained, for example, when you attempt to extract the square root from -2. Not a valid floating-point number or invalid instruction (input value outside the valid value range)
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The following table shows the signal state of the bits in the status word for the results of instructions with floating-point numbers that do not lie within the valid range: The number zero is represented with e = m = 0 e = 255 and m = 0 stands for "infinite."įloating-point numbers according to the ANSI/IEEE standard The largest floating-point number = 2-2 to the power of (-23) * 2 to the power of (254-127) = 2-2 to the power of (-23) * 2 to the power of (+127) The smallest floating-point number = 1.0 * 2 to the power of (1-127) = 1.0 * 2 to the power of (-126) Using the floating-point format shown above, the following results: S: for a positive number, S = 0 and for a negative number, S = 1. This means that an additional sign is not required for the exponent. m * 2 to the power of (e - bias)īias: bias = 127. Using the three components S, e, and m, the value of a number represented in this form is defined by the formula: The following table shows the values of the individual bits in floating-point format. The three components together occupy one double word (32 bits): The whole number part of the mantissa is not stored with the rest, because it is always equal to 1 within the valid number range.
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The exponent e = E + bias, increased by a constant (bias = +127) They consist of the following components: For example, when forming the sum of two numbers, the exponents must be matched by shifting the mantissa (hence floating decimal point) since only numbers with the same exponent can be added.įloating-point numbers in STEP 7 conform to the basic format, single width, described in the ANSI/IEEE standard 754-1985, IEEE Standard for Binary Floating-Point Arithmetic. The disadvantage is in the limited accuracy of calculations. With the limited number of bits for the mantissa and exponent, a wide range of numbers can be covered. This type of number representation has the advantage of being able to represent both very large and very small values within a limited space. Numbers in floating-point format are represented in the general form "number = m * b to the power of E." The base "b" and the exponent "E" are integers the mantissa "m" is a rational number. Format of the Data Type REAL (Floating-Point Numbers) Format of the Data Type REAL (Floating-Point Numbers)