Most modern computer systems operate using binary logic. The computer represents values using two voltage levels (usually 0V for logic 0 and either +3.3 V or +5V for logic 1).

With two levels we can represent exactly two different values. These could be any two different values, but by convention we use the values zero and one. These two values, coincidentally, correspond to the two digits used by the binary number system.

The weighted values for each position is determined as follows:

2⁷	2⁶	2⁵	2⁴	2³	2²	2¹	2⁰	2^-1	2^-2
128	64	32	16	8	4	2	1	.5	.25

In the United States among other countries, every three decimal digits is separated with a comma to make larger numbers easier to read.

For example, 123,456,789 is much easier to read and comprehend than 123456789.

We will adopt a similar convention for binary numbers. To make binary numbers more readable, we will add a space every four digits starting from the least significant digit on the left of the decimal point.

For example, the binary value 1010111110110010 will be written 1010 1111 1011 0010

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