What is the relationship between base and number of digits? - Mathematics Stack Exchange
For example, to represent the number in base 10, we know we place a 3 in the the video hardware in your computer can convert those numbers to electrical signals If we have three bits, we can represent 8 different combinations. . commit the base 2 factors to memory as an aid to quickly correlate the relationship. There are 10 types of people in this world: Those who can read binary and those This is a brief instructable on what numbers represent and how to convert. Introduces the concepts behind different number bases, and shows how to convert between decimal (base ten) and binary (base two) numbers.
- Chapter 2. Binary and Number Representation
- Number Systems and Bases
- pH and pKa relationship for buffers
Hex and binary are similar, but tick over every 16 and 2 items, respectively. Try converting numbers to hex and binary here: It was uphill both ways, through the snow and blazing heat.
Enter the Romans In Roman numerals, two was one, twice.
Numbers in Different Bases | The Oxford Math Center
Three was one, thrice: And of course, there are many more symbols L, C, M, etc. The key point is that V and lllll are two ways of encoding the number 5.
Give each number a name Another breakthrough was realizing that each number can be its own distinct concept. Rather than represent three as a series of ones, give it its own symbol: Do this from one to nine, and you get the symbols: In our number system, we use position in a similar way.
We always add and never subtract.
Chapter 2. Binary and Number Representation
And each position is 10 more than the one before it. Our choice of base 10 Why did we choose to multiply by 10 each time? Most likely because we have 10 fingers. Imagine numbers as ticking slowly upward — at what point do you flip over the next unit and start from nothing?
Enter zero And what happens when we reach ten? Suffice it to say, Zero is one of the great inventions of all time. Look how unwieldly their numbers are without it. But before we go to the Henderson-Hasselbalch equation, which I am gonna assume you've seen before, and if not we have some other videos introducing it and also deriving it, let's do a quick review of what exactly is a buffer.
So a buffer is something that contains an aqueous solution.
It's something that contains both a weak acid, which generically we write as HA, and it also contains in equilibrium the conjugate base of our acid, so A minus. And it just has a special name, 'cause it happens to be for the dissociation of an acid.
And as you can see up here, an acid and its conjugate base are just related by the fact that the acid has an extra H. We can rearrange the Henderson-Hasselbalch equation to get a lot of different kinds of information.
Numbers in Different Bases
One kind of problem you see a lot is for some buffer, you know, they might ask you, oh, what's the pH? The other thing that you can use the Henderson-Hasselbalch equation to tell you is the relationship between A minus and HA which is something you might wanna know. A lot of times, you just wanna know, you know, what's in your solution, depending on what you wanna do to your solution, if you wanna add things to it, maybe you wanna add some acid, you wanna add some base.
You wanna know what's going on. The Henderson-Hasselbalch equation gives you a really quick and easy way of doing that. So what we're gonna do, is we're gonna rearrange this equation to solve for this ratio that we might be interested in. And I don't know about you, but I actually find, well, laughs I find logs not super-intuitive sometimes.
So I'm actually going to get rid of the log by raising both sides to the 10th power. So what does this tell us? It may not look like it tells us a whole lot more, but actually, it tells us a lot. It tells us about the relative relationship and size between A minus and HA concentration. So if we look at this, we can derive a couple relationships.