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Unformatted text preview: CSCI 120 Introduction to Computation Its only a matter of representation (draft) Saad Mneimneh Visiting Professor Hunter College of CUNY 1 From bits to binary Consider the number thirteen (nothing special about this number, but I picked it because I was born on that day). Now imagine I ask you to write the number thirteen on the board. You would most definitely write the following expression: 13 But, if you want, you could also write the expression: thirteen What guides you to make the decision? It is a system of representation . Clearly, when someone says the number thirteen, you know that we are most likely talking about numbers. So you invoke the system of representation for numbers. It happens to be the decimal system (a 10 digit alphabet). But you certainly understand what thirteen is. It is a word in English that represents the number thirteen. Therefore, it is the same thing but using another alphabet (a 26 digit, or letter as commonly called, alphabet). You even have more representations for number thirteen! You can imagine thirteen apples or thirteen oranges as a mental representation of that number. Therefore, thirteen is just a concept. You can express this concept in many ways. The fact that we use the decimal system more frequently is merely a biological coincidence (we have 10 fingers to count!). Unfortunately, computers are less lucky. The way they evolved did not give them the chance to stick to the decimal system. Recall that the computer memory is just a reservoir of bits. Therefore, any concept must be represented using 0s and 1s only. Most importantly, and in particular, numbers. That should not be a problem. We simply have to enrich our system of representations by adding one more representation or alphabet for numbers. The bits will serve as our digits (or letters) in this new alphabet. We call it the binary alphabet, or the binary number system (bi for two). Before you get the chance to be surprised by the idea, note that it is possible to represent numbers using two digits only, namely 0 and 1. In fact, why be surprised at all? We can do it with only one digit after all. Heres how: zero one 00 two 000 three 0000 four 00000 five 000000 six 0000000 seven 00000000 ....
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- Spring '09