Convert a Ratio of Integers (Base Conversion »)

Conversion Tool

From:	Initial Base
	Numerator
	Denominator
To:	New Base:


Result: (Ratio in New Base)

Help

Examples

From			To	Result
Initial Base	Numerator	Denominator	New Base	Result
10	35	8	2	(100.011)₂
2	100011	1000	10	(4.375)₁₀
10	6877	198	10	(34.732)₁₀
16	A345F	9C	2	(1000010111110.11110111110010)₂
16	A345F	9C	8	(10276.75745)₈
7	1	64	3	(0.00012021122)₃
23	{16}	1{17}	2	(0.0110)₂
10	7867	90001	15	(a lot of digits—try it!)

"Initial Base" Entry

Enter the initial base of the numerator and denominator (e.g., 2 for binary, 8 for octal, 10 for decimal, 16 for hexadecimal, etc.)

"Numerator" and "Denominator" Entries

Enter the ratio you want to convert to the new base. If the initial base of the ratio is between 2 and 16, you may use the digit symbols in the following tables to encode the numerator and denominator (note that the digit values are in base 10).

Digit Value	Digit Symbol
0	0
1	1
2	2
3	3
4	4
5	5
6	6
7	7

Digit Value	Digit Symbol
8	8
9	9
10	a or A
11	b or B
12	c or C
13	d or D
14	e or E
15	f or F

For any base (larger than 16 or not), you can always enter the numerator and denominator as sequences of base 10 digit values contained inside braces. The following table gives some examples of how you could enter the base 10 ratio 6775 / 4391.

Base	Numerator	Denominator
10	6775	4391
2	1101001110111	1000100100111
16	1A77	1127
16	{1}{10}{7}{7}	{1}{1}{2}{7}
30	{7}{15}{25}	{4}{26}{11}

"New Base" Entry

Enter the new base to which the ratio is converted (e.g., 2 for binary, 8 for octal, 10 for decimal, 16 for hexadecimal, etc.)