How Do You Convert A Decimal (Base-10) Number Into Any Other Base?
The number system we use every day is called “base 10” (or “decimal”) because it has ten possible place values (zero through nine). Sometimes another number base is more convenient, though. Computer systems, for example, often use base-2 (“binary), base-8 (“octal”), or base-16 (“hexadecimal”) counting systems. This tutorial will show you how to convert an everyday decimal number into any other number base. Write down all the powers of the base you’re converting TO– starting with one (the “zero power”)– that are less than (or equal to) the number you’re working with. For example, if you’re converting 315 to base-4, you’d write down these values: 4^0 = 1; 4^1 = 4; 4^2 = 16; 4^3 = 64; 4^4 = 256. “Prepare” your final answer by writing down a series of BLANKS for EACH POWER you wrote down in Step 1. Label each blank with its proper place value, from largest to smallest. So, to convert 315 to base-4, we’d write five blanks: __ 4^4 = 256 __ 4^3 = 64 __ 4^2 = 16 __ 4^1 = 4 __ 4^0 = 1 Divide
