# 32 bit single precision IEEE 754 binary floating point number 1 - 1000 0001 (2023)

## 32 bit single precision IEEE 754 binary floating point 1 - 1000 0001 - 010 1000 0000 0000 0000 0000 to decimal system (base ten) = ?

### 4. Convert the mantissa from binary (base 2) to decimal (base 10):

#### Mantissa represents the number's fractional part (the excess beyond the number's integer part, comma delimited).

010 1000 0000 0000 0000 0000(2) =

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

 Number 1 - 1000 0001 - 010 1000 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 26 01:41 UTC (GMT) Number 0 - 0111 1110 - 011 0011 0011 0011 0000 1110 converted from 32 bit single precision IEEE 754 binary floating point to decimal number (float) in decimal system (in base 10) = ? May 26 01:40 UTC (GMT) Number 1 - 1000 0111 - 010 1110 0000 0000 0000 0111 converted from 32 bit single precision IEEE 754 binary floating point to decimal number (float) in decimal system (in base 10) = ? May 26 01:39 UTC (GMT) Number 1 - 1000 0000 - 110 0111 1100 0000 0000 1010 converted from 32 bit single precision IEEE 754 binary floating point to decimal number (float) in decimal system (in base 10) = ? May 26 01:39 UTC (GMT) Number 0 - 1000 0011 - 001 1011 1110 0010 1001 1000 converted from 32 bit single precision IEEE 754 binary floating point to decimal number (float) in decimal system (in base 10) = ? May 26 01:39 UTC (GMT) Number 0 - 1010 1100 - 001 1000 0000 0000 0000 0011 converted from 32 bit single precision IEEE 754 binary floating point to decimal number (float) in decimal system (in base 10) = ? May 26 01:38 UTC (GMT) Number 1 - 1000 0000 - 111 0100 0100 0000 0001 1001 converted from 32 bit single precision IEEE 754 binary floating point to decimal number (float) in decimal system (in base 10) = ? May 26 01:38 UTC (GMT) Number 1 - 0101 1100 - 011 0001 0010 1111 1111 0111 converted from 32 bit single precision IEEE 754 binary floating point to decimal number (float) in decimal system (in base 10) = ? May 26 01:38 UTC (GMT) Number 0 - 0000 0000 - 110 0110 1000 0000 0001 0010 converted from 32 bit single precision IEEE 754 binary floating point to decimal number (float) in decimal system (in base 10) = ? May 26 01:37 UTC (GMT) Number 1 - 0000 0000 - 000 0000 1000 0000 0000 0001 converted from 32 bit single precision IEEE 754 binary floating point to decimal number (float) in decimal system (in base 10) = ? May 26 01:37 UTC (GMT) Number 0 - 1000 1000 - 100 0010 0001 1111 1110 1011 converted from 32 bit single precision IEEE 754 binary floating point to decimal number (float) in decimal system (in base 10) = ? May 26 01:36 UTC (GMT) Number 1 - 0100 1011 - 010 1100 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 26 01:36 UTC (GMT) Number 0 - 1000 0001 - 101 1011 1010 1011 1111 0100 converted from 32 bit single precision IEEE 754 binary floating point to decimal number (float) in decimal system (in base 10) = ? May 26 01:35 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)

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