The biggest issue with the “table method” shown on the previous page is that it is hard to translate into an algorithm that a machine could run. The multiplication/division methods shown on this page are much easier to express in simple terms as they rely on mathematics instead of looking at a table and making a decision.
Step 1: Start with a blank answer and the number you are converting Step 2: Divide your number by 2 to make
a quotient and a remainder Step 3: Place your remainder on the left side of your answer Step 4: If your quotient
is 0, you are done Otherwise, make the quotient your new number and go back to step 2
Here is an example of running the algorithm to convert \({11}_{10}\) to binary:
Step 1: Start with the 'number' you are converting and the 'answer' of 0 Step 2: Multiply your 'answer' by
2 Step 3: Remove the leftmost digit of 'number' and add it to your 'answer' Step 4: If 'number' has no more
digits, you are done Otherwise, go back to step 2
If we follow this algorithm to convert \({1101}_{2}\) into a decimal value, it would look like this:
Step 1: 'number' is 1101 and 'answer' is 0 Step 2: 'answer' is multiplied by 2 - it becomes 0 Step 3:
Remove the leftmost digit of 'number' and add it to 'answer' 'number' is now 101 and 'answer' is 1 Step 4:
'number' still has digits, go back to step 2 Step 2: 'answer' is multiplied by 2 - it becomes 2 Step 3: Remove
the leftmost digit of 'number' and add it to 'answer' 'number' is now 01 and 'answer' is 3 Step 4: 'number'
still has digits, go back to step 2 Step 2: 'answer' is multiplied by 2 - it becomes 6 Step 3: Remove the
leftmost digit of 'number' and add it to 'answer' 'number' is now 1 and 'answer' is 6 Step 4: 'number' still has
digits, go back to step 2 Step 2: 'answer' is multiplied by 2 - it becomes 12 Step 3: Remove the leftmost digit
of 'number' and add it to 'answer' 'number' is now "" (empty) and 'answer' is 13 Step 4: 'number' is empty. We
are done, the 'answer' is 13.
As mentioned earlier, the advantage of this algorithm is that it very easily converts into relatively simple computer code. To demonstrate that, the algorithm is implemented in Python in the codelens below. You DO NOT need to worry about exactly how the Python language works. You will notice that turning the English algorithm above into code requires some changes, but the code shown follows the same process described above. See the “tips” box below the code lens for help running the program.
Use can use the large gray scroll bar beneath the code to scroll the code to the right - at the end of each line of code is an explanation of what that line “says”
\({2}_{11010}\) is 26 in decimal. You can check your answer by making sure it equals 13 in decimal. But you shouldn’t have to do math to figure out the answer.
