How can you interpret binary code?

Answer 1

Binary is not actually a code, but a different way of recording numbers. It actually works exactly the same way as our usual decimal notation, but with one key difference.

First, consider the number 275. When we look at that number there are three digits, which we normally refer to as the ones column, the tens column, and the hundreds column. We call them these names because the digits don't actually represent their own value, but a multiple of it. We can also express that number as:

200 + 70 + 5

or:

2×100 + 7×10 + 5×1

Which is the same as saying:

2×102 + 7×101 + 5×100

In other words, each column in a number does not actually represent the value of that digit shown, but that value multiplied by ten to the power of the column number, with the columns numbered zero and up going from right to left. For instance, the number 8675309 can be expanded as:

8×106 + 6×105 + 7×104 + 5×103 + 3×102 + 0×101 + 9×100

This is why we refer to it as base ten notation.

Binary, or base two notation, works exactly the same way, but with one difference. Instead of having ten unique digits (0-9), we only have two of them (0-1). This means that instead of using powers of ten for our columns, we use powers of two. Instead of having columns of ones, tens, hundreds, etc. we have ones, twos, fours, eights, and so on.

Going back to our original example number then, 275, it would be expressed in binary as:

100010011

To convert that number back to decimal, all you need to do is add up the powers of two that correspond with the digits that have a value of one. In this case, we have:

1×28 + 0×27 + 0×26 + 0×25 + 1×24 + 0×23 + 0×22 + 1×21 + 1×20

= 28 + 24 + 21 + 20

= 256 + 16 + 2 + 1

= 275