A method of performing floating-point conversions in a digital computing system includes determining a source coefficient, c1, and a source exponent, n, of an input value represented by a floating-point number in a source base, b1; converting the source coefficient to a common base, b2, and storing the converted coefficient in a first digit collection; iteratively multiplying the contents of the first digit collection by b1 and storing the intermediate results therein, wherein one or more overflow bits of the first digit collection are carried and added to one or more additional digit collections once a nonzero value is reached; and an output value in the common base is stored in the digit collections after n multiplication iterations, represented by c2×b2m, wherein c2 is the converted coefficient of the output value in the common base b2 and m is the exponent of the output value.