Computers store information with transistors or “switches” that have an on (“1”) or off (“0”) state. As a result, they must perform mathematical and logical operations using a binary (base-2) numbering system. For example, as can be see above, computers represent our the decimal/base-10 number **“113”** with the binary/base-2 number: **“1110001”**.

These different numbering systems are different “counting-unit sets” analogous to “poker chips.” For example, for base-10 **“113″** you’d have 3 different types of chips/units for each power of 10: **“100”**, **“10”**, **“1”** and you can use 0-9 of each to count “113” = 1x**“100”** + 1x**“10”** + 3x**“1”**.

Similarly, for the binary number **“1110001”** you’d use 6 different types of chips/units for each power of 2. As such, you can convert a decimal number to a binary number by “factoring” the decimal number into the sum of several powers of 2 and then representing each power of 2 position as either a 1 or 0.

This work by Eugene Douglass and Chad Miller is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.