Denary to binary conversion
On the previous page we saw how a binary number has a value depending on the arrangement of 1s and 0s in the number.
It should be apparent that the same number can be represented in the denary system as well.
We shall now describe a method of converting any denary number from 0 to 255 into its equivalent binary number.
We will be using denary number 211 in our example
Step 1.
Start off with the table below that has all zeros in the second row.
Step 2.
Is 211 larger than 128?
If yes, put a 1 underneath the 128 in the table. If not, leave it at 0.
Step 3.
As we put a 1 under 128, subtract 128 from 211 to see what is left:
211 - 128 = 83
Step 4.
We have 83 left
Is 83 larger than 64? If yes, put a 1 in the space under 64, if not, leave it at 0.
Step 5.
We started with 83 and we put a 1 under 64. Thus, subtract 64 from 83 to see what is left:
83 - 64 = 19
Step 6.
We have 19 left.
Is 19 larger than 32? If yes, put a 1 in the space under 32, if not, leave it at 0.
Step 7.
As 19 was NOT larger than 32, we left it at 0.
Is 19 larger than 16? If yes, put a 1 in the space under 16, if not, leave it at 0.
Step 8.
We started with 19 and we put a 1 under 16. Thus, subtract 16 from 19 to see what is left:
19 - 16 = 3
Step 9.
We have 3 left.
Is 3 larger than 8? If yes, put a 1 in the space under 8, if not, leave it at 0.
Step 10.
As 3 was NOT larger than 8, we left it at 0.
Is 3 larger than 4? If yes, put a 1 in the space under 4, if not, leave it at 0.
Step 11.
As 3 was NOT larger than 4, we left it at 0.
Is 3 larger than 2? If yes, put a 1 in the space under 2, if not, leave it at 0.
Step 12.
We started with 3 and we put a 1 under 2. Thus, subtract 2 from 3 to see what is left:
3 - 2 = 1
Step 13.
Is there a 1 left over? If yes, place a 1 in the space under 1, if not leave it at 0.
There was a 1 left over and so a 1 was placed in the last position.
ANSWER:
Using the method above, the denary number has been converted to its equivalent binary: 11010011
