Data Processing and Number Systems: Processing Data in Computer

In this article, I have combined the notes I took while researching the subject of data processing in the computer. In the article, I talked about binary and decimal number systems, which are the basic number systems, and explained the properties of different number systems. The most commonly used number systems are binary, octal, decimal, and hexadecimal. I also gave information about symbolic representations of non-numeric data. Finally, I touched on the importance of bits and bytes, and I also touched on the topic of Recursion.

Subjects:

• Basic Number Systems
• Common Number Systems
• Retention of Non-Digital Data on the Computer
• Bits
• Converting Bytes to Bits
• Recursion

Basic Number Systems

There are commonly two number systems; Binary and Decimal number systems.

The binary number system consists of the binary number system. Binary numbers are obtained by writing the numbers in base 2. Therefore, all numbers are expressed using the numbers 0 and 1.

Since our range is from 0 to 9 in the decimal number system, we can express 10 different cases in a single digit. In binary, on the other hand, 2 different states are expressed in a single digit.

Common Number Systems

In computer science, different number systems are used. Depending on the type of number systems, each digit can be a power of a particular number. The power of a number means repeating that number multiplied by itself a certain number of times.

For example, ²³ (2 to the 3rd power) expresses the number 2 multiplied by itself 3 times, resulting in the value 8.

The most commonly used number systems are:

1. Binary number system: The binary number system, the basic number system used by computers, uses only the digits 0 and 1. In this number system, each digit is a power of 2.
2. Decimal number system: The decimal number system, the most commonly used number system by humans, uses 10 digits from 0 to 9. In this number system, each digit is a power of 10. For example, the number 352 consists of 3 hundreds, 5 tens, and 2 ones digits combined.
3. Octal number system: The octal number system, another number system often used in computer science, uses 8 numbers from 0 to 7. In this number system, each digit is a power of 8.
4. Hexadecimal number system: The hexadecimal number system, which is another number system used in computers and other systems, uses the letters A, B, C, D, E, and F, as well as numbers from 0 to 9. In this number system, each digit is a power of 16.

Processing of Non-Digital Data on the Computer

Non-numeric data can be represented by symbols. For example, when we convert the number 1100010010 to the decimal base, its value is 786, but if we analyze it as a symbol, not a number, it can be the letter “W”.

Another example, we have the symbol 100101010, which might correspond to the letter “V”.

This is usually done using character encodings, markup languages or image processing techniques. For example, a text document is represented and processed on the computer by character encodings, while an image file is converted into numerical data using a special format. This numerical data is then made workable by the processor, memory, disk drive, and other computer components. At the end of the process, non-numeric data can be converted back into symbolic representations and presented to users.

Bits

Due to its nature, the amount of data that can be kept inside the computer is limited. The smallest building blocks of this data are bits. We can think of these bits as memory. The more bits, the less data storage space is left.

1 Byte = 8 bits

Converting Bytes to Bits

The conversion of bytes to bits is done by multiplying the number of bytes by 8.

For example, when we want to express 2 bytes of data in bits, we multiply 2 by 8 and we get 16 bits.

Similarly, to express 4 bytes of data in bits, we multiply 4 by 8 and we get 32 bits.

In general, converting bytes to bits can be easily done by multiplying the number of bytes by 8.

Recursion

Recursion is the repeated execution of a function by calling itself. This method is a technique used in programming languages and is included in the structure of many algorithms.

The calculation of a problem by dividing it into sub-problems, the expressions where we specify where it will end, we call Recursion.
Recursion works by specifying a condition for a function’s operations to be resolved. When this condition is met, the function stops calling itself and returns to complete its operations. These operations are processed in the order in which the function is called, and their results are aggregated.

Recursion is especially used in algorithms where recursive operations such as tree structures are made. In this way, it is ensured that the code is more understandable and simple. However, using recursion incorrectly can cause infinite loops and crash the program. Therefore, the use of recursion should be well planned and controlled.

Summary

• There are two most well-known number systems; Binary and Decimal number systems. In the binary number system, numbers are written in base 2. Therefore it is expressed using 0 and 1. In the decimal number system, our range is from 0 to 9. We can express 10 different situations
• Common number systems can be diversified as Decimal number system, Binary number system, Octal number system, Hexadecimal number system.
• When non-numerical data such as a text document is represented and processed on the computer by character encodings, an image file is converted into numeric data using a special format. This numerical data is then rendered processable by the processor and its other components. At the end of the process, non-numeric data can be converted back into symbolic representations and presented to users.
• Bits are the smallest building blocks of data.
• In general, converting bytes to bits can be easily done by multiplying the number of bytes by 8.
• Recursion is the repeated execution of a function by calling itself.