Number System Study Guides

Courses : Digital Logic Lecturer : Czachary Semester : 4thSemester, 2022/2023 Session Number System The number system is a way of representing numbers using certain symbols. There are several number systems that are commonly used, including the decimal, binary, octal, and hexadecimal number systems. 1. Decimal Number System: The decimal number system is the most commonly used system in everyday life. This system uses 10 symbols, namely the numbers 0 to 9. The numbers in the decimal number system are represented by digits placed in certain positions. Each position represents a multiple of 10, going from right to left. For example, the number 356 in the decimal system means 6 units, 50, and 3 hundred. 2. Binary Number System: The binary number system uses base 2 and uses only two symbols, namely 0 and 1. This system is often used in computers and digital technology, because electronic circuits can represent two states, namely off (0) and on (1). Binary numbers are represented by positioned binary digits, representing multiples of 2, from right to left. For example, the number 1010 in the binary system means 0 units, 1 two, 0 four, and 1 eight. 3. Octal Number System: The octal number system uses base 8 and uses eight symbols, namely the numbers 0 through 7. Octal numbers are represented by octal digits placed in certain positions, representing multiples of 8, from right to left. This system is not as popular as the decimal or binary systems, but it is still used occasionally in computer programming. For example, the number 127 in the octal system means 7 units, 24, and 1 one hundred and twenty eight. 4. Hexadecimal Number System: The hexadecimal number system uses base 16 and uses 16 symbols, namely the numbers 0 through 9 and the letters A through F (used to represent the numbers 10 through 15). This system is often used in computer programming and in color representation in computer graphics. A hexadecimal number is represented by positioned hexadecimal digits, representing multiples of 16, from right to left. For example, the number 3F in the hexadecimal system means 15 units and 3 sixteen. Other number systems may also exist, depending on the base used and the symbols accepted. However, the systems mentioned above are the most common and are often used in a variety of contexts. Besides the number systems mentioned earlier, there are several other number systems worth noting: 1. Roman Number System: The Roman number system uses a combination of several Latin letter symbols to represent numbers. These symbols include I (1), V (5), X (10), L (50), C (100), D (500), and M (1000). The value of the numbers is determined by the combination and arrangement of these symbols. The Roman numeral system is still used in some historical contexts, calculating dates, and in some special cases. 2. Base-N Number System: In addition to the decimal (base 10), binary (base 2), octal (base 8), and hexadecimal (base 16) number systems, there is also a base-N number system. In this system, N represents the base used and numbers are represented using the symbols from 0 to N-1. For example, the base-12 number system uses the symbols 0 through 9 and the letters A through B to represent the numbers 10 through 11. The base-N number system is not as common as the systems previously mentioned, but they can be used in some special domains. 3. Infinite Number System: The infinite number system has no limit on the numeric values it can represent. In mathematics, infinite numbers are often used in the context of concepts such as limits, infinite series, and infinite sets. However, in implementations of computing, infinity is often expressed as a very large value or using a special representation such as "Infinity". Understanding these different number systems is important in areas such as mathematics, computing, engineering and science. Each number system has its own uses depending on the context, and choosing the right number system can affect the efficiency and suitability of an application or problem solver. In conclusion, a number system is a way of representing numbers using certain symbols. Commonly used number systems include the decimal, binary, octal, and hexadecimal number systems. The decimal number system is the most commonly used in everyday life, while the binary number system is often used in computers and digital technology. Apart from that, there are also other number systems such as the Roman numeral system, which uses the Latin letter symbols, and the base-N number system, where N represents the base used. There is also an infinite number system that is used in mathematics to represent an infinite number of values. Understanding these different number systems is important in many fields, including mathematics, computing, engineering, and science. Choosing the right number system can affect the efficiency and suitability of an application or problem solving.