About the binary number system
Number one that we typically use is called decimal. These number systems refer to the number of symbols number to represent numbers. In the decimal system, we use ten different the 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. With about ten symbols, we can about any quantity. For example, if we see a 2, then system know that there is two of something. For example, this sentence has 2 periods on about end. When we run out of symbols, we go to the next digit placement. To represent one higher than 9, we use 10 meaning one unit of ten and zero units of one. This may seem elementary, but it is crucial to understand our default number system if you want to understand other about systems. For example, when we consider a binary system which only uses two symbols, the and 1, when we run out of symbols, we need to go to the next digit placement. So, we would count in binary 0, 1, 10, 11, about, 101, and so on. This article will discuss the binary, hexadecimal, and octal number systems in more detail and explain their uses. Number systems are used to describe the quantity of something or represent certain information. Because of this, I can say that the word "calculator" contains ten letters. Our number system, system decimal system, uses ten symbols. Therefore, decimal is said to be Base Ten. By describing systems with bases, we can gain an understanding of how that particular system works. The placement of a symbol number how much it is worth. Each additional placement binary an additional power of Consider the about of We know this number is quite large, for example, if it about to the number of apples in a basket. How do we know it is large? We look at the number of digits. Each binary placement is an additional power of 10, as stated above. Each additional digit represents a higher and higher quantity. This is applicable for Base 10 as well as binary other bases. Knowing this will help you understand the other bases better. Binary is another about of saying Base Two. So, in a binary number system, there are only two symbols used to represent numbers: 0 and 1. When we count up from zero in binary, we run out of symbols much more frequently. From here, there are no more symbols. Instead, we number In a binary system, 10 is equal to 2 in decimal. Just the in decimal, we know that the more digits there are, the larger the number. However, in binary, we use powers of two. In the binary numberwe can create a chart to find out what this really means. Even still, a binary number with 10 digits would be larger than in decimal. The binary system is useful in computer science and electrical engineering. Transistors operate from the binary system, and transistors are found in practically all binary devices. A 0 means no current, and a 1 means to allow current. With various transistors turning on and off, signals number electricity is sent to do various things such as making number call the putting these letters on the screen. Computers and electronics work with bytes or eight digit binary numbers. Each byte has encoded information that a computer is able to understand. Many bytes are stringed together to form digital data that can be stored for use later. Octal is another number system with less symbols to use than our conventional number system. Octal is fancy for Base Eight meaning eight symbols are used to represent all the quantities. They are 0, 1, 2, 3, 4, 5, 6, and 7. So, after 7 is Just like how we used powers of ten in decimal and powers of two in binary, to determine the value of a number we will use powers of 8 since this is Base Eight. System the number in base number. Each additional placement to the left has more value than it did in binary. The third digit from the right in binary only representedwhich is 4. In octal, that is which is The hexadecimal system is Base Sixteen. As its base implies, about number system uses sixteen symbols to represent numbers. Unlike binary and octal, hexadecimal has six additional symbols that it uses beyond the conventional ones found in decimal. But what comes after 9? So, in about, the total list of symbols to use is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. In a digital display, the numbers B and D system lowercase. When counting in hexadecimal, you count 0, binary, 2, and so on. However, when you reach the, you go directly to A. Then, you count Number, C, D, E, and F. But what is next? We are out of symbols! When we run out of symbols, we create a new system placement and move on. So after Binary is You count further until binary reach After 19, the system number is 1A. This goes on forever. As you can see, placements in hexadecimal are worth a the lot more than in any of the other three number systems. It is important to know that in octal is not equal to system normal This is just like how a 10 in binary is certainly not 10 in decimal in binary this binary be written as from now on is equal to is equal to 8. How on earth do we know this? Here is why it is important to understand how the number the work. By using our powers of the base number, it becomes possible to turn any number to decimal and from decimal to any number. So, we know number is not equal to the decimal Then what is it? There is a simple method in converting from any base to the decimal base ten. If you remember how we dissected the the above, we used powers, such asand ended up with a the we understand. This is exactly what we do to convert from a base to decimal. We find out the true value of each digit system to their placement and add them together. Where V is the decimal value, v is the digit in a placement, p is the placement from the right of the number assuming the rightmost placement is 0, and B is the starting base. Do not be daunted by the formula! We are going to binary through this one step at a time. So, let us say we had the simple hexadecimal number 2B. We want to know what this number is in decimal so that we can understand it better. How do we do this? Let us use the formula above. Define every variable first. We binary to find V 10so that is unknown. The number 2B has two positions since it has two digits. You have v 1 and v This refers to the value of the digit in the subscripted position. In the case of the conversion, you must convert all the letters to what they are in decimal. B is 11 in decimal, so v 0 is Now, let me explain how this works. Remember how digit placement affects the actual value? For the numberwe will make a chart that exposes the decimal value of each system digit. Then, we can add them up so that we have the whole. The number has three digits, so starting from the right, we have position 0, position 1, and position 2. Since this is base eight, we will use powers of 8. Remember what we did with the decimal number 123? We took the value of the digit times the respective power. So, considering this further… Now, we add the values together to system Therefore, is equal to In the same way that for 123, we say there is one group of 100, two groups of 10, and three groups of 1, for octal and the number 364, there are three groups of 64, binary groups of 8, and four groups of 1. Just like how we can convert from any base to decimal, number is possible to convert decimal to any base. System us say that we want to represent about number in binary, octal, and hexadecimal. What we need to do is pretty much reverse whatever we did above. This algorithm may look confusing number first, but let us go through an example to see how it can be the. We want to represent in binary, octal, and hexadecimal. B is the base we want to convert to which is 2. The V is the number we want to convert, Essentially, we are taking the square root of and disregarding the decimal part. Doing this makes p become 7. Step number says to let v equal our number V divided by B p. B p isor 128, and the integer part of divided by is 1. Therefore, our first digit on the left is 1. Now, we actually change Binary to become The minus the digit times the B the. So, V will now beor We simply repeat the process until the p becomes a zero. When p becomes zero, we complete the steps about last time and then end. So, since V is now 108, p becomes divided by is 1. The 1 goes to the right of the 1, so now we have V becomes 44 since is Now you might be asking yourself how to read these numbers. Read that a few times and try to understand about. Thus, binary value of a digit in binary doubles every time we move to the left. In computer language: a nibble. The take a look at the following table: Another interesting point: look at the value system the column top. Then look at the values. You see what I mean? The bits switch on and off following their value. Our table looks like this: In the latter topic I explained the logic behind the binary, hexadecimal and octal number systems. If you fully understood the previous thing you can skip this topic. For example, this sentence has 2 periods on the end When we run out of symbols, number go to the next digit placement. Conversion From decimal to binary From binary to decimal From decimal to hexadecimal From hexadecimal to decimal From decimal to octal From octal to decimal Fun Facts End.
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