Definition of Bicimals
The bicimals can be referred to as the rational binary numbers.
A bicimal is the base-two analog of a decimal;
it has a bicimal point and bicimal places, and can be terminating or repeating.
Like decimals, bicimals are created from fractions through long division.
Also like decimals, bicimals can be converted back to fractions.
You convert a bicimal to a fraction the same way you convert a decimal to a fraction, you just work in binary instead of decimal, and use powers of two instead of powers of ten.
Converting a bicimal fraction into a Decimal Fraction
The process of converting a binary fraction into its decimal equivalent is done in two steps with the numbers the left-hand and right-hand sides of the radix point separately.
When looking at converting the binary on the left-hand side of the radix point we convert it just as we would when converting any binary integer number into its decimal equivalent.
Example
101 in base 2= (1×2 squared) + (0 times 2 power 1) + (1 ×2 power0)
= (1×4)+ (0 ×2)+ (1 ×1)=5
Next, we work out the chunk at the right-hand side of the radix point.
We do exactly the same thing here as we did on the left, just with the fractional columns:
?0.101?in base 2= (1×2power (-1)) + (0 ×2power (-2)) + (1 ×2power (-3))
= (1×1 half) + (0 ×1 quarter) + (1 ×1 over 8)
= (1×0.5)+ (0 ×0.25)+ (1 ×0.125)=?0.625?in base 10
??0.101?in base 2= ?0.625?in base10
So we have a fractional part that represents 0.625 in base 10.
So we now combine the integer part (5) and fractional parts (0.625) together on either side of the radix point.
This gives us the number 5.62510.
A terminating bicimal is always easy to convert to a fraction: the numerator of the resulting fraction is the bicimal itself, treated as an integer; the denominator is 2n, where n is the number of bicimal places.
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