| Converting binary to denary
If we look at a denary number like 8328, we see that it contains two eights. Now these two figures look identical however closely we examine them, but we know that they are different. The 8 on the right-hand end is really 8 but the other one is actually 8000 because it is in the thousands column.
The real value of a digit is dependent on two things: the digit used and the column in which it is placed.
In the denary system, the columns, starting from the right, are units, tens,
hundreds, thousands etc. Rather than use these words, we could express
them in powers of ten. A thousand is 10 10 10 = 103 and in a similar
way, a hundred is 102, ten is 101 and a unit is 100. Each column simply
increases the power applied to the base of the number system.
Columns in a binary world also use the base raised to increasing powers as we move across the columns towards the left.
So we have:
23 22 21 20
The denary equivalent can be found by multiplying out the powers of two. So 23 is 2 2 2 = 8 and 22 = 4, 21 = 2 and finally 20 = 1. Starting from the right-hand side, the column values would be 1, 2, 4, 8 etc. Let’s use this to convert the binary number 1001 into denary.
Method
Step 1: Write down the values of the columns
8 4 2 1
Step 2: Write the binary number underneath
8 4 2 1
1 0 0 1
Binary - the way micros count
Step 3: Evaluate the values of the columns
8 1 = 8
4 0 = 0
2 0 = 0
1 1 = 1
Step 4: Add up the values
8 + 1 = 9
As we have seen, all the columns containing a binary 0 can be ignored because they always come out to 0 so a quicker way is to simply add up all the column values where the binary digit is 1.
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