64bit IEEE 754: Double Precision Floating Point Binary -> Double: Converter of 64 Bit Double Precision IEEE 754 Binary Floating Point Standard Representation Numbers, Converting and Writing Them as Base Ten Decimal System Numbers (Double)
Convert 64 bit double precision IEEE 754 binary floating point standard numbers to base ten decimal system (double)
A number in 64 bit double precision IEEE 754 binary floating point standard representation...
... requires three building elements: sign (it takes 1 bit and it's either 0 for positive or 1 for negative numbers), exponent (11 bits), mantissa (52 bits)
The latest 64 bit double precision IEEE 754 floating point binary standard numbers converted and written as decimal system numbers (in base ten, double)
How to convert numbers from 64 bit double precision IEEE 754 binary floating point standard to decimal system in base 10
Follow the steps below to convert a number from 64 bit double precision IEEE 754 binary floating point representation to base 10 decimal system:
1. Identify the elements that make up the binary representation of the number: First bit (leftmost) indicates the sign, 1 = negative, 0 = pozitive. The next 11 bits contain the exponent. The last 52 bits contain the mantissa.
2. Convert the exponent, that is allways a positive integer, from binary (base 2) to decimal (base 10).
3. Adjust the exponent, subtract the excess bits, 2(11 - 1) - 1 = 1,023, that is due to the 11 bit excess/bias notation.
4. Convert the mantissa, that represents the number's fractional part (the excess beyond the number's integer part, comma delimited), from binary (base 2) to decimal (base 10).
5. Put all the numbers into expression to calculate the double precision floating point decimal value: (-1)Sign × (1 + Mantissa) × 2(Exponent adjusted)
Example: convert the number 1 - 100 0011 1101 - 1000 0000 0010 0001 0100 0000 0100 1110 0000 0100 0000 1010 1000 from 64 bit double precision IEEE 754 binary floating point system to base ten decimal (double):
1. Identify the elements that make up the binary representation of the number:
First bit (leftmost) indicates the sign, 1 = negative, 0 = pozitive. The next 11 bits contain the exponent: 100 0011 1101 The last 52 bits contain the mantissa: 1000 0000 0010 0001 0100 0000 0100 1110 0000 0100 0000 1010 1000
2. Convert the exponent, that is allways a positive integer, from binary (base 2) to decimal (base 10):
3. Adjust the exponent, subtract the excess bits, 2(11 - 1) - 1 = 1,023, that is due to the 11 bit excess/bias notation: Exponent adjusted = 1,085 - 1,023 = 62
4. Convert the mantissa, that represents the number's fractional part (the excess beyond the number's integer part, comma delimited), from binary (base 2) to decimal (base 10):
1 - 100 0011 1101 - 1000 0000 0010 0001 0100 0000 0100 1110 0000 0100 0000 1010 1000 converted from 64 bit double precision IEEE 754 binary floating point representation to a decimal number (float) in decimal system (in base 10) = -6 919 868 872 153 800 704(10)