64 bit double precision IEEE 754 binary floating point number 0 - 000 0000 0000 - 0000 0000 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 converted to decimal base ten (double)
64 bit double precision IEEE 754 binary floating point 0 - 000 0000 0000 - 0000 0000 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 to decimal system (base ten) = ?
1. Identify the elements that make up the binary representation of the number:
First bit (the leftmost) indicates the sign, 1 = negative, 0 = positive.
The next 11 bits contain the exponent: 000 0000 0000
The last 52 bits contain the mantissa: 0000 0000 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111
2. Reserved bitpattern.
Notice that all the exponent bits are on 0 (clear) and at least one of the mantissa bits is on 1 (set).
This is one of the reserved bitpatterns of the special values of: Denormalized.
Denormalized numbers are too small to be correctly represented so they approximate to zero. Depending on the sign bit, -0 and +0 are two distinct values though they both compare as equal (0).
3. Convert the exponent from binary (base 2) to decimal (base 10):
Convert 64 bit double precision IEEE 754 floating point standard binary numbers to base ten decimal system (double)
64 bit double precision IEEE 754 binary floating point standard representation of numbers requires three building blocks: sign (it takes 1 bit and it's either 0 for positive or 1 for negative numbers), exponent (11 bits), mantissa (52 bits)
Latest 64 bit double precision IEEE 754 floating point binary standard numbers converted to decimal 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)