**32-bit Single Precision** = [ Sign bit ] + [ Exponent ] + [ Mantissa (32 bits) ]

**First convert 324800 to binary.**

324800_{10 }= 01001111010011000000_{2}

**Convert the binary number into base 2 scientific notation.**

01001111010011000000 = 1 . 001111010011000000 x 2^{18}

**Determine the sign bit.**

- Positive number takes 0 as sign bit
- Negative number takes 1 as sign bit

Since 324800 is a positive number, our **sign bit is 0**. This will be the first bit out of the 32 total bits in the IEEE 754 single precision representation.

**Get the exponent based on precision**

1 . 001111010011000000 x 2^{18 }

There are a set of biases for both single and double precision. The exponent bias for **single precision is 127. **Adding 127 to the base 2 exponent, we get **127 + 18 = 145 (Single Precision).**

**Convert the exponent to binary**

145_{10 }=** ****10010001**_{2}

Write in standard form:** 10010001 = ****1 . 0010001 x 2**^{7}

**Mantissa = ****0010001 **(decimal part of the exponent in binary)

**Combine the calculated values into one final number. Add trailing zeros to get 32 bits in total**

**32-bit Single Precision** = [ Sign bit ] + [ Exponent ] + [ Mantissa (32 bits) ]

**0** **10010001 ****00100010000000000000000**

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