Octal Number System

Courses : Digital Logic Lecturer : Czachary Semester : 4thSemester, 2022/2023 Session Octal Number System The Octal Number System is a number system that uses base 8, which means it consists of 8 digits, namely 0, 1, 2, 3, 4, 5, 6, and 7. This number system is often used in programming and computing, especially in systems based on eight. In the octal number system, each digit has a value associated with a power of 8. The rightmost digit in an octal number represents 8 to the power of 0 (1), the next digit represents 8 to the power of 1 (8), the next digit represents 8 to the power of 2 (64), etc. For example, the octal number 247 can be interpreted as 7 units (7x8^0), 4 tens (4x8^1), and 2 hundreds (2x8^2). So 247 in the octal number system has the same overall value as 7 + 32 + 128 = 167 in the decimal system. Conversions between decimal and octal numbers are also possible. To convert a decimal to octal number, we can use the repeated division method with base 8, whereas to convert an octal number to decimal, we multiply each octal digit by the multiple of 8 according to the position of the digit and add them up. The octal number system has uses in the representation and management of data in computing, especially in situations where the use of base 8 is more efficient or relevant. However, in the development of modern computer technology, the octal number system tends to be replaced by other number systems such as binary and hexadecimal which are more commonly used. Understanding of the octal number system is still important in some special contexts, such as programming certain hardware or understanding the internal structure of a computer system. However, in general programming and data processing, the octal number system is rarely used widely. In the octal number system, conversions between binary and octal numbers are also common. Each octal digit can be represented by three binary digits. For example, the octal digit 3 could be represented by the binary digit 011, the octal digit 5 could be represented by the binary digit 101, and so on. Conversion from octal to binary is done by mapping each octal digit to the corresponding three binary digits. Then, the binary digits can be combined to form the binary representation of the octal number. In contrast, conversion from binary to octal is accomplished by dividing the binary digits into groups of three digits, then converting each group of three binary digits to the corresponding octal digit. The octal number system has several uses in specialized fields such as hardware programming, signal processing, and numbering systems in some communications networks. However, in general, the octal number system is rarely used in everyday computing. In the octal number system, arithmetic operations such as addition, subtraction, multiplication, and division can also be performed with rules similar to those of other number systems. For example, when adding two octal numbers, we add up the digits sequentially, and if there is a carry (addition) that exceeds 7, then that carry will be used in adding the next digit. Examples of addition in the octal number system: 43 + 56 -----121 In the example above, we added the rightmost digit first (3 + 6 = 11), so we wrote 1 and carry 1. Then, we added the next digit (4 + 5 + 1 (carry) = 10), so we write the number 0 and carry 1. Finally, we write the remaining carry 1. Thus, the sum of the octal numbers 43 and 56 is 121 in the octal number system. Apart from arithmetic operations, logical operations can also be performed in the octal number system. Logical operations such as AND, OR, XOR, and NOT can be applied to each bit of an octal number to obtain the desired logical result. Although the octal number system has special uses in some fields, such as hardware programming and signal processing, its use has waned with developments in computer technology. The octal number system is generally replaced by other number systems that are more commonly used such as the decimal number system and the binary number system. In conclusion, the octal number system is a base 8 number system consisting of the digits 0 through 7. Arithmetic operations and logical operations can be performed in the octal number system with rules similar to those of other number systems. Although rarely used in everyday computing, an understanding of the octal number system is still relevant in some specialized fields and can aid in programming hardware and understanding the internal structure of computer systems.