A real number bx is approximated in machine by a rational:
x = (−1)s × m × β
e
where
β is the radix
10 in your calculator and (usually) your head
2 in most computers
Some IBM financial mainframes use radix 10, why ?
s ∈ {0,1} is a sign bit
m is the mantissa, a rational number of nm digits in radix β


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