1025 words - 4 pages

Do you remember watching the movie, The Matrix? Do you remember the green columns of zeroes and ones that were streaming down the screen? Those ones and zeros are part of a numbering system called Binary. Binary is a simple system that only utilizes two character symbols but accomplishes large counting tasks. Binary is not a number system you would want to use for everyday tasks because there are no shortcuts, you have to do the equation the same way every time and it takes a long time to do most calculations. That is why we use what is called the Denary (AKA Decimal) number system. The Denary number system is called a base-10 system as opposed to Binary being called a base-2 system. Base-10 means that the system uses ten different characters as symbols, 0-9. As stated above Binary uses only two character symbols, 0-1. The chart below should demonstrate how the two system look compared to one another.

Denary Binary Denary Binary

1 1 11 1011

2 10 12 1100

3 11 13 1101

4 100 14 1110

5 101 15 1111

6 110 16 10000

7 111 17 10001

8 1000 18 10010

9 1001 19 10011

10 1010 20 10100

Binary has operations just like the Denary system has. Binary addition is the operation that is the most basic and also should give the best example of how the system works. In the Denary system addition works by placing one digit above the other and adding there values. The same goes for Binary. The only difference is how you add zeros and ones. If one has 1+0 or 0+1 the answer is 1. Or if one 0+0 the answer one would get is 0. That all is straight forward but when one gets 1+1 the answer is 10. The reason for this is because there is not a 2 in Binary, but if there were it is 10. Examples of each systems addition is below.

Denary Binary

5 101

+ 4 + 100

_______ _________

9 1001

As one can see Binary looks very confusing but both problems are identical in numerical value. This is why Binary is not effective enough for use in everyday calculations. Humans can only remember digits in order up to seven digits. After the seventh digit is reached it becomes very hard to remember. Because of this it would make normal calculations hard. People would have to write every problem just make sure they are carrying the correct digits. Conversion of Binary to Denary is very easy once you get the general notion of how it works. Converting Binary as simple as adding together the ones in the number a multiplying them by their place by two. As one may remember from elementary school, the inherent value of a number is judged by what column it is in. These columns being ones, tens, hundreds, thousands, so on and so forth. For example, if a seven is placed in the tens column it has a higher value than a seven that is placed in the ones column, because the seven in the tens column is multiplied by ten. In Binary, where a one is placed is similar to where that seven may have been to give it...

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