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I have this example on how to convert from a base 10 number to IEEE 754 float representation
Number: 45.25 (base 10) = 101101.01 (base 2) Sign: 0 Normalized form N = 1.0110101 * 2^5 Exponent esp = 5 E = 5 + 127 = 132 (base 10) = 10000100 (base 2) IEEE 754: 0 10000100 01101010000000000000000 This makes sense to me except one passage:
45.25 (base 10) = 101101.01 (base 2) 45 is 101101 in binary and that's okay.. but how did they obtain the 0.25 as .01 ?
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"Radix point" is a general term that applies to all number bases. In base 10 notation, the radix point is more commonly called the decimal point, where the prefix deci- implies base 10. Similarly, the term "binary point" is used for base 2.
In a positional numeral system, the radix or base is the number of unique digits, including the digit zero, used to represent numbers. For example, for the decimal/denary system (the most common system in use today) the radix (base number) is ten, because it uses the ten digits from 0 through 9.
In English-speaking countries, the decimal point is usually a small dot (.) placed either on the baseline or halfway between the baseline and the top of the digits In many other countries, the radix point is a comma (,) placed on the baseline.
Simple place value. In base 10, you have these places:
... 103 102 101 100. 10-1 10-2 10-3 ...
... thousands, hundreds, tens, ones . tenths, hundredths, thousandths ...
Similarly, in binary (base 2) you have:
... 23 22 21 20. 2-1 2-2 2-3 ...
... eights, fours, twos, ones . halves, quarters, eighths ...
So the second place after the . in binary is units of 2-2, well known to you as units of 1/4 (or alternately, 0.25).
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