Converter of 32 bit single precision IEEE 754 binary floating point standard system numbers: converting to base ten decimal (float)

Convert 32 bit single precision IEEE 754 floating point standard binary numbers to base ten decimal system (float)

A number in 32 bit single 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 (8 bits), mantissa (23 bits)

Latest 32 bit single precision IEEE 754 floating point binary standard numbers converted to decimal base ten (float)

Number 1 - 1000 0000 - 010 1001 0011 1111 1111 1110 converted from 32 bit single precision IEEE 754 binary floating point to decimal number (float) in decimal system (in base 10) = ? May 29 16:29 UTC (GMT)
Number 0 - 0000 0000 - 101 0000 0000 0000 0000 0000 converted from 32 bit single precision IEEE 754 binary floating point to decimal number (float) in decimal system (in base 10) = ? May 29 16:29 UTC (GMT)
Number 0 - 0000 0000 - 000 0000 0000 0000 1001 0110 converted from 32 bit single precision IEEE 754 binary floating point to decimal number (float) in decimal system (in base 10) = ? May 29 16:28 UTC (GMT)
Number 1 - 0000 0011 - 100 1011 0000 0000 0000 1110 converted from 32 bit single precision IEEE 754 binary floating point to decimal number (float) in decimal system (in base 10) = ? May 29 16:28 UTC (GMT)
Number 1 - 1111 1110 - 000 0000 0000 0000 0000 0000 converted from 32 bit single precision IEEE 754 binary floating point to decimal number (float) in decimal system (in base 10) = ? May 29 16:27 UTC (GMT)
Number 0 - 1000 0101 - 011 1011 1011 1111 1111 1101 converted from 32 bit single precision IEEE 754 binary floating point to decimal number (float) in decimal system (in base 10) = ? May 29 16:26 UTC (GMT)
Number 0 - 0000 0110 - 100 1011 1111 1111 1111 0110 converted from 32 bit single precision IEEE 754 binary floating point to decimal number (float) in decimal system (in base 10) = ? May 29 16:25 UTC (GMT)
Number 0 - 0000 0000 - 110 1100 1000 0100 0011 0101 converted from 32 bit single precision IEEE 754 binary floating point to decimal number (float) in decimal system (in base 10) = ? May 29 16:24 UTC (GMT)
Number 0 - 0111 1101 - 110 0001 1010 1011 1001 1001 converted from 32 bit single precision IEEE 754 binary floating point to decimal number (float) in decimal system (in base 10) = ? May 29 16:24 UTC (GMT)
Number 1 - 1000 0111 - 001 0101 0101 1110 0001 0110 converted from 32 bit single precision IEEE 754 binary floating point to decimal number (float) in decimal system (in base 10) = ? May 29 16:21 UTC (GMT)
Number 0 - 1110 0000 - 001 0000 0000 0000 0001 0000 converted from 32 bit single precision IEEE 754 binary floating point to decimal number (float) in decimal system (in base 10) = ? May 29 16:20 UTC (GMT)
Number 1 - 1010 0000 - 000 1001 0001 0111 1111 1111 converted from 32 bit single precision IEEE 754 binary floating point to decimal number (float) in decimal system (in base 10) = ? May 29 16:19 UTC (GMT)
Number 0 - 0111 1011 - 011 1010 1101 0010 0100 1000 converted from 32 bit single precision IEEE 754 binary floating point to decimal number (float) in decimal system (in base 10) = ? May 29 16:17 UTC (GMT)
All base ten decimal numbers converted to 32 bit single precision IEEE 754 binary floating point

How to convert numbers from 32 bit single precision IEEE 754 binary floating point standard to decimal system in base 10

Follow the steps below to convert a number from 32 bit single precision IEEE 754 binary floating point representation to base 10 decimal system:

  • 1. Identify the three elements that make up the binary representation of the number:
    First bit (leftmost) indicates the sign, 1 = negative, 0 = pozitive.
    The next 8 bits contain the exponent.
    The last 23 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(8 - 1) - 1 = 127, that is due to the 8 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 single precision floating point decimal value:
    (-1)Sign × (1 + Mantissa) × 2(Exponent adjusted)

Example: convert the number 1 - 1000 0001 - 100 0001 0000 0010 0000 0000 from 32 bit single precision IEEE 754 binary floating point system to base 10 decimal system (float):

  • 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 8 bits contain the exponent: 1000 0001
    The last 23 bits contain the mantissa: 100 0001 0000 0010 0000 0000
  • 2. Convert the exponent, that is allways a positive integer, from binary (base 2) to decimal (base 10):
    1000 0001(2) =
    1 × 27 + 0 × 26 + 0 × 25 + 0 × 24 + 0 × 23 + 0 × 22 + 0 × 21 + 1 × 20 =
    128 + 0 + 0 + 0 + 0 + 0 + 0 + 1 =
    128 + 1 =
    129(10)
  • 3. Adjust the exponent, subtract the excess bits, 2(8 - 1) - 1 = 127, that is due to the 8 bit excess/bias notation:
    Exponent adjusted = 129 - 127 = 2
  • 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):
    100 0001 0000 0010 0000 0000(2) =
    1 × 2-1 + 0 × 2-2 + 0 × 2-3 + 0 × 2-4 + 0 × 2-5 + 0 × 2-6 + 1 × 2-7 + 0 × 2-8 + 0 × 2-9 + 0 × 2-10 + 0 × 2-11 + 0 × 2-12 + 0 × 2-13 + 1 × 2-14 + 0 × 2-15 + 0 × 2-16 + 0 × 2-17 + 0 × 2-18 + 0 × 2-19 + 0 × 2-20 + 0 × 2-21 + 0 × 2-22 + 0 × 2-23 =
    0.5 + 0 + 0 + 0 + 0 + 0 + 0.007 812 5 + 0 + 0 + 0 + 0 + 0 + 0 + 0.000 061 035 156 25 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 =
    0.5 + 0.007 812 5 + 0.000 061 035 156 25 =
    0.507 873 535 156 25(10)
  • 5. Put all the numbers into expression to calculate the single precision floating point decimal value:
    (-1)Sign × (1 + Mantissa) × 2(Exponent adjusted) =
    (-1)1 × (1 + 0.507 873 535 156 25) × 22 =
    -1.507 873 535 156 25 × 22 =
    -6.031 494 140 625
  • 1 - 1000 0001 - 100 0001 0000 0010 0000 0000 converted from 32 bit single precision IEEE 754 binary floating point representation to decimal number (float) in decimal system (in base 10) = -6.031 494 140 625(10)