5 Binary

Binary is just another way to say base-2. The significance of binary representation is due to the nature of most digital computers. Most digital computers represent information using the states of billions (will become trillions and etc.) of transistors, and each transistor can only have two states: on and off.

Consequently, it is handy to assign the value of 1 to the on-state, and the value of 0 to the off-state. With each transistor only able to represent a 0 or a 1, a group of transistors can represent values in base-2.

The conversion from base-2 to base-10 is no different from the approach already described in section 3, and the conversion from base-10 to base-2 is no different from the approach already described in section 4. However, due to the nature of binary numbers, both methods can be done quicker then an arbitrary base.