Computer Number | Precision in Computer vs Precision in Mathematics
Regardless of how powerful the computer may be, it is still finite. This means that the computer takes a finite time to complete an operation, and that it has only a finite amount of space in which to store things.
Bit : the problem faced by computer designers is how to represent an arbitrary number using a finite amount of memory. Most computer memories contain magnetic materials in which elementary magnets are aligned to face either up or down. As a consequence, the most elementary units of computer memory are the two binary integers 0 and 1 that form the basis of the binary number system (representing all numbers with just two symbols). The phrase “binary integer” is usually abbreviated as the word bit. This in turn means that, ultimately, everything stored in a computer memory is just a long string of zeros and ones, with each bit representing the number of times a power of 2 is to be added in. While it is no longer essential that you know how to convert numbers between different representations in order to compute, it is essential to remember that numbers on a computer are stored using a finite number of bits, and that unless the number is a power of 2, the process of converting it to a decimal number introduces a small uncertainty. In computing, an uncertainty is often called an “error”, although this does not imply that anyone or any computer has done anything wrong.
Byte : the number of bits that a computer or its operating system uses to store a number is called the word length. For example, you might have heard about 32 bit and 64 bit versions of the Windows operating systems. Well, these just refer to the length of the words that the computer processes. While we are talking about these sorts of things, we should mention that often word lengths or memory sizes are expressed in bytes (a mouthful of bits), where 1 byte = 8 bits = B. Conveniently, 1 byte is the amount of memory needed to store a single letter like “a’’. This adds up to a typical printed page requiring approximately 3000 B = 3 KB of storage. Of course with memory sizes continuing to grow, rather than bytes, you hear of kilobytes, megabytes or gigabytes, which mean one thousand, one million or one billion bytes (giga is used for a billion since in Europe a billion means a million millions rather than our thousand millions).
Precision and accuracy are two ways that scientists think about error. Accuracy refers to how close a measurement is to the true or accepted value. Precision refers to how close measurements of the same item are to each other. Precision is independent of accuracy. That means it is possible to be very precise but not very accurate, and it is also possible to be accurate without being precise. The best quality scientific observations are both accurate and precise.
Accuracy is defined as “the degree to which the result of a measurement conforms to the correct value or a standard’ and essentially refers to how close a measurement is to its agreed value.
Precision is defined as ‘the quality of being exact” and refers to how close two or more measurements are to each other, regardless of whether those measurements are accurate or not. It is possible for precision measurements to not be accurate.
Both accuracy and precision reflect how close a measurement is to an actual value, but they are not the same. Accuracy reflects how close a measurement is to a known or accepted value, while precision reflects how reproducible measurements are, even if they are far from the accepted value. Measurements that are both precise and accurate are repeatable and very close to true values.
Accurately hitting the target means you are close to the centre of the target, even if all the marks are on different sides of the centre. Precisely hitting a target means all the hits are closely spaced, even if they are very far from the centre of the target.
In computer science, the precision of a numerical quantity is a measure of the detail in which the quantity is expressed. This is usually measured in bits, but sometimes in decimal digits. It is related to precision in mathematics, which describes the number of digits that are used to express a value. Precision is often the source of rounding errors in computation. The number of bits used to store a number will often cause some loss of accuracy. An example would be to store “sin(0.1)” in IEEE single precision floating point standard. The error is then often magnified as subsequent computations are made using the data (although it can also be reduced).
In mathematics, precision describes the level of exactness in a number’s digits. For example, the number 54.6 has precision 1 (one decimal digit). A number with end zeroes (“00”) has a negative precision, such as 500 having precision -2, or 4,000 as precision -3. A whole number (not ending in “0”) has precision 0. The level of precision differs from the word “accuracy” of a number, which means the correctness or truth of a number as used to describe an item or count.
Precision engineering is where parts that have high specifications are created and need to be engineered in a precise way, hence the name. With high precision machinery and computer technology, any part can be created through different techniques and technology that engineering has to offer, and there are many different advantages of using precision engineering. Only precision engineering can handle the demand of technology with the finer requirements and mass production. Many people don’t think about the precision that goes into making parts, whether they are large or small, precision engineering takes place in different industries such as nuclear and aerospace. Precision engineering ensures a longer running life along with less wear or fatigue, giving a better lifespan compared to manually manufactured parts.
Having a longer running life reduces costs and means lower running costs overall, the whole production speed is faster and needs fewer inspections. It is highly reliable as mass production can be achieved; it also eliminates human error, helping with safety.
