# Single precision floating point binary calculation process

Exercise: Convert 469.357 to a raw binary floating point representation

# Sign
0 (Because 0 if positive, 1 if negative)

==> Sign = 0

# Exponent and Mantissa
### Convert the whole part into binary (WholeBinary)
469 / 2 = 234    1 (Because 469 / 2 has a reminder (atlikums) = 1)
234 / 2 = 117      0
117 / 2 = 58      1
58 / 2 = 29.      0
29 / 2 = 14.      1
14 / 2 = 7.         0
7 / 2 = 3.         1
3 / 2 =  1          1
1 / 2 = 0          1

WholeBinary = 111010101 (Read from bottom up)

### Convert the fraction into binary (FractionBinary)
0.357 * 2 = 0.714 0 (If you multiply by 2 and the result is larger than 1, then write down 1, otherwise 0)
0.714 * 2 = 1.428 1
0.428 * 2 = 0.856 0 (Once you go over one in the results, remove the one, e.g. 1.428 -> 0.428)
0.856 * 2 = 1.712 1
	…..
(Continue till you’re out of space or smth - enough to later fill all 32 bits including mantissa and sign)

FractionBinary = 010110110110010

### Convert the binary number into a normalized binary scientific notation (e.g. 1.0000010101 * 2^12)
NumberBinary = 111010101 . 010110110110010 (WholeBinary . FractionBinary)
NumberBinaryScientific = 1 . 11010101010110110110010 * 2 ^ 8 (NumberBinary in scientific notation)

==> Mantissa = 11010101010110110110010 	(NumberBinaryScientific without the leading zero)
==> Exponent = 8 + 127 = 135 = 10000111 			(NumberBinaryScientific exponent + 127 in binary)

# All together
Floating binary format = Sign Exponent Mantissa

==> Full Single-precision floating binary 	= 0 10000111 11010101 010110110110010
==>Online converter result 				= 0 10000111 11010101 010110110110010

Conclusion - you did it correctly!

### Sidenote
Online converter here = https://www.exploringbinary.com/floating-point-converter/
Use "Single precision" and "Raw binary format"