Besides it seeming uncomfortably hard to imagine currently, what other implications would this have? Perhaps the most important implication is that we would have had another increment beyond 9 in the 1s column. We would be naturally using a system of Base11. Let's, for a moment, imagine that we had 11 fingers. It would instead be a single-digit representation of 10. This actually brings us to our introduction of Base16. "If binary is all that computers are made of, how would you write letters in binary?" Good question. So, let's take the arbitrary number 1001101 in binary, and apply this formula. (2 raised to the power of the column from the right -1) * (the number found in the column) And on that note, this is why these systems are referred to as Base(N). So, how does binary work? Take the formula from above, and instead of using ten, use two. Binary is the most basic system needed for all logical operations (think "true" and "false"). This lends itself well to computing for many reasons, most fundamentally because computers rely on switches that have two states: on or off. The next system we will talk about is Base2, or binary. This is why these systems are referred to as Base(N). We can see that there this is a generalizable formula for understanding all base systems. Therefore, if there is a 6 in the 5th column from the right, 10^4*6 = 60,000. (10 raised to the power of the column from the right -1) * (the number found in the column) A generalized function to understand Base10, then, is as follows: Starting from the right, we can understand this as "0*1 + 2*10 + 0*100 + 1*1000". We all know this piece of the pizzle.Ĭonsider the number 1020. This is continued, and if the tens column is at 9 and the 1s column is at 9, 1 is added to the 100's column, and so forth. Specifically, the 1s column increases from 0-9, and then another ten is added to the tens column. So as each column fills up, the next column is then increased by one, and we start back at the previous column to fill it up again in the same manner as before. In other words, "000008" is the same as "8". For all intents and purposes, we can postulate that there are an infinite number of leading zeros before our first significant column. So we move to the next column (to the left), and start at 1. Once the ones column is full (has 9), that is the maximum for the column. Starting at 0, we count up to 9, filling the "1's" column. This will be the foundation of understanding that we'll use in the subsequent discussion. So, let's talk a bit about how Base10 actually is structured. This makes it much easier to understand the system. In fact, it is most likely because of the learning process we decided above - we have 10 fingers. So, why did we choose Base10? It's not because the letterforms 0-9 exist that was actually a result of the choice to use Base10. At each stage we will discuss the advantages and uses for each type. Finally, we'll finish things up by talking about Base32 and Base64. In this article, we'll start by gaining a more rounded understanding of Base10 and its structure, then we will discuss binary (Base2, the building blocks of computing). No one ever attempts to enlighten us that we are actually making some more complex mathematical assumptions we all know Base10, to be precise. At a young age, we learn to count on our fingers - starting out with 1-5, then 1-10, and maybe, if you're particularly enterprising as a toddler, you will learn to count to 20, 30, and beyond.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |