Number Base Change

Changing from a base to any other base is accomplished by

Separating the number into two parts - Integer Part and the Fractional Part
Divide the Integer Part by the new base to obtain a Quotient and Remainder
The Remainder is the Last digit of the number in the new base
Divide the Quotient just obtained, by the new base Obtaining a new Quotient and Remainder
The Remainder is the next digit of the number in the new base
Repeat this procedure until the Quotient is zero

Now the Fractional Part

Multiply the Fractional Part by the new base
The Integral Part of the product is the First digit to the left of the decimal point in the Fractional Part of the new base
Drop the Integral Part and repeat the previous two stepsfor the desired decimal places or the product becomes only an Integer

Convert 8765.4321 to base 8
8765 Integral Part	.4321 Fractional Part	New Number in New Base
8765/8 = 1095 r 5	.4321*8 = 3.4568	5.3
1095/8 = 136 r 7	.4568*8 = 3.6544	75.33
136/8 = 17 r 0	.6544*8 = 5.2352	075.335
17/8 = 2 r 1	.2352*8 = 1.8816	1075.3351
2/8 = 0 r 2	.8816*8 = 7.0528	21075.33517

This will continue for a lot of digits. (Somewhere it must repeat, I think. I'll look into it.) If you wish to change to binary first change to base 8 because the number of steps is less than dividing by 2. Any power of 2 works. 8 is convenient because the remainder is 0 through 7. Where 16 has remainders of 0-9, a, b, c, d, e, and f. Change from a base to another base that is a power of the base is simple. Since 2³ = 8, all we need to do is convert each octal (base 8) digit to binary and then regroup.

21075.33517 base 8 equals 10 001 000 111 101 . 011 011 101 001 111 base 2
To change to base 16 regroup into groups of 4 from the decimal point, since 2⁴ = 16
10 0010 0011 1101 . 0110 1110 1001 1110 base 2
223d.6e9e base 16