The binary numbering system has only two digits, 1 and 0. At first glance, this may seem like a severe limitation. Computers seem to get along fine with it though. At the most basic level, computers work with only bits of information represented by ones and zeroes. These bits, in groups of eight, are referred to as bytes. Each byte has 256 possible combinations of ones and zeroes. To get a feel for how this works, try counting to 15 (the first binary digit is always zero) using only four digits.

## Video of the Day

#### Step

Write 0000 on a piece of paper. This represents 0 in standard decimal notation. Write the remaining numbers in a column directly underneath this first entry to get an idea of how this works. Write the decimal value to the right of the column to keep track of your count.

#### Step

Write 0001 under your first entry. This represents the decimal value 1.

#### Step

Write 0010 as the next entry. This is the point where binary and decimal values cease to be the same. The binary value of 0010 is the decimal value 2. This may look like the decimal value for ten (10) but in binary, the value of each place is multiplied by a factor of two from the highest possible value of the previous place. Since the highest possible value in a single position when using 0 and 1 is 1, you must add a digit to the left of the current position to add a value.

#### Step

Write 0011 in the binary column. This represents 0010 plus 0001 or 3. That is two, 0010 in binary, plus one, 0001 in binary.

#### Step

Write the next number, 0100, in the binary column. This is the binary representation of 4 or, two times the highest possible value for the previous position. The first 1 in the left-most position always signifies the highest numerical value for the set. The right-most 1 is the lowest value. So, add 1 to 0100 to make the binary value for 5.

#### Step

Write 0101 in the binary column. Adding 1 to 0100 makes the decimal value 5.

#### Step

Write 0110 in the binary column. Notice that you dropped the final 1 and replaced it with 10 or the decimal value 2. In essence you have added 0100 (4) and 0010 (2) to get the value 0110 (6).

#### Step

Write 0111 in the binary column. Adding the 0001 (1) to 0110 (6) gives you the decimal value 7.

#### Step

Fill in the remaining values to 1111, decimal value 15, in the binary column using the same method of adding and subtracting binary values. The binary numbers from 7 to 15 are: 0111 (7); 1000 (8); 1001 (9); 1010 (10); 1011 (11); 1100 (12); 1101 (13); 1110 (14); 1111 (15).