1. Binary Numbers Press any key to begin.

2. In order to understand the binary numbering system lets first look at our decimal system. The decimal numbering system consists of the numbers 0 through 9. 0 1 2 3 4 5 6 7 8 9 01 After nine we place a 1 in the tens column and start again with 0. Which gives us 10. The decimal system is also known as base 10 because it is based on the 10 numbers 0 – 9. Press any key to continue…

3. Binary Numbers have only two digits 0 or 1 DecimalBinary 0 0 1 1 2 10 3 11 4 100 5 101 6 110 7 111 Binary is known as Base 2 Press any key to continue…

4. As you can see it would take a lot of time to create charts to represent Binary numbers. An easier way is to use the powers of 2 2 7 =128 2 6 = 64 2 5 = 32 2 4 = 16 2 3 = 8 2 2 = 4 2 1 = 2 2 0 = 1 Lets place the above calculations into a chart that will make it easy to convert a binary number to a decimal number. Press any key to continue…

5. 0 0 1 0 1 0 0 1 1 x 1 = 1 Total = 41 128 x 0 = 0 64 x 0 = 0 32 x 1 = 32 16 x 0 = 0 8 x 1 = 8 4 x 0 = 0 Use the chart to convert the binary number to decimal. Note: The bit to the far right is the Least Significant Bit (LSB) and will determine if the number is even or odd. 2 x 0 = 0 Press any key to continue…

6. 0 1 1 1 1 1 1 1 1 x 1 = 1 Total = 127 128 x 0 = 0 64 x 1 = 64 32 x 1 = 32 16 x 1 = 16 8 x 1 = 8 4 x 1 = 4 Use the chart to convert the binary number to decimal. 2 x 1 = 2 Note: if consecutive bits from the right are all 1’s Then the answer is the next power of 2 minus 1 In this case 128 – 1 = 127 Press any key to continue…

7. 1 0 1 1 1 0 1 0 1 x 0 = 0 Total = 186 128 x 1 = 128 64 x 0 = 0 32 x 1 = 32 16 x 1 = 16 8 x 1 = 8 4 x 0 = 0 Take a piece of paper and convert the binary number to decimal. Press any key when you have the answer. 2 x 1 = 2 Press any key to continue…

8. The largest number that can be represented using an 8 bit binary number is 255. 1 1 1 1 1 1 1 1 Remember the rule – if all the digits are 1 then the number is the next power of 2 minus 1 256 – 1 = 255

9. Converting a binary number to a decimal number is a simple task if you understand the chart below and how to use it. The End