Binary Numbers Press any key to begin.

In order to understand the binary numbering system lets first look at our decimal system. 0 1 2 3 4 5 6 7 8 9 The decimal numbering system consists of the numbers 0 through 9. 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. 1 Press any key to continue…

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

An easier way is to use the powers of 2 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 20 = 1 24 = 16 21 = 2 25 = 32 22 = 4 26 = 64 23 = 8 27 =128 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…

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

Use the chart to convert the binary number to decimal. 0 1 1 1 1 1 1 1 1 x 1 = 1 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 4 x 1 = 4 8 x 1 = 8 16 x 1 = 16 32 x 1 = 32 64 x 1 = 64 128 x 0 = 0 Total = 127 Press any key to continue…

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

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

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