Number system in computer

Hexadecimal Number System The hexadecimal number system is a type of number system, that has a base value equal to 16. It is also pronounced sometimes as ‘hex’. Hexadecimal numbers are represented by only 16 symbols. These symbols or values are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F. Each digit represents a decimal value. For example, D is equal to base-10 13. Hexadecimal number systems can be converted to other number systems such as binary number (base-2), octal number (base-8) and decimal number systems (base-10). The concept of the The list of 16 hexadecimal digits with their equivalent decimal, octal and binary representation is given here in the form of a table, which will help in number system conversion. This list can be used as a translator or converter also. Hexadecimal Number System Table Below is the table of hexadecimal number systems with equivalent values of the binary and decimal number systems. Decimal Numbers 4-bit Binary Number Hexadecimal Number 0 0000 0 1 0001 1 2 0010 2 3 0011 3 4 0100 4 5 0101 5 6 0110 6 7 0111 7 8 1000 8 9 1001 9 10 1010 A 11 1011 B 12 1100 C 13 1101 D 14 1110 E 15 1111 F Below is the link to download the table. Students can download the PDF and learn offline too. Hexadecimal Number System Conversions As we know, there are 16 digits in the hexadecimal number system, represented from 0 to 9 same as decimals, but after that, it starts with an alphabetical representation of preceding numbers such as A, B, C, D and E. Let...

In daily lives, people often have to depict, represent or associate certain things or objects with a quantity. This is because of the fact that assigning quantities to certain values or aspects in life makes it easier to compare them with other similar aspects. For example, a teacher grading students’ papers would not label each paper with adjectives like “good”, “better”, “awesome” or “poor”, etc., rather would assign a certain numerical value to that paper based on the student’s performance so that it is easy to assess the knowledge and preparation level of the student, but if the former approach were to be applied, it would lead to utter confusion and no accurate comparison could be made out of it. Since at some point, the teacher would run out of adjectives that are relevant to this particular situation, and it would lead to the same words being used to grade all the unique answers/ responses given by the students. Situations like these call for, rather necessitate the usage of a unique method of valuation, which not only helps recognize the true worth of the object in question but also represents it fairly and non- ambiguously. Such a system which uses certain words or symbols to quantify a given object or value is called the number system. Number A number refers to a word or symbol which represents a particular quantity. It is with the help of numbers only that multiple arithmetic operations are performed and we have been able to develop so much in the field of physi...

A binary number system is one of the four types of number systems, and it is used to define a number in a binary system. A binary number system represents a number in terms of only two digits, i.e., 0 (zero) and 1 (one). In the word “binary”, “bi” means “two”. As a result, this draws the line back to the representation of a number using the numbers 0 and 1 only. The base-2 numeral system is used to represent binary numbers. For example, (1101) 2 is a binary number where 2 is the radix. Each digit in the binary number system is said to be a “bit”. This number system is widely used in computers. All inputs given to a computer are decoded by it into a series of 0’s or 1’s before being processed further since a computer can only understand binary information, which is represented by the numbers 0 or 1. It is simple to convert a decimal number into a binary number and vice-versa. The notations for decimal numbers and binary numbers are different. For example, a decimal is represented as (15) 10 where 10 is the base of the decimal number, and the corresponding binary number is represented as (1111) 2 where 2 is the base of a binary number. 10001 8 1000 18 10010 9 1001 19 10011 10 1010 20 10100 Binary to Decimal Conversion A binary number is converted into a decimal number by multiplying each digit of the binary number by the power of either 1 or 0 to the corresponding power of 2. Let us consider that a binary number has n digits, B = a n-1…a 3a 2a 1a 0. Now, the corresponding de...

Computers don’t understand words or numbers the way humans do. Modern software allows the end user to ignore this, but at the lowest levels of your computer, everything is represented by a binary electrical signal that registers in one of two states: on or off. To make sense of complicated data, your computer has to encode it in binary. Binary is a base 2 number system. Base 2 means there are only two digits—1 and 0—which correspond to the on and off states your computer can understand. You’re probably familiar with base 10—the decimal system. Decimal makes use of ten digits that range from 0 to 9, and then wraps around to form two-digit numbers, with each digit being worth ten times more than the last (1, 10, 100, etc.). Binary is similar, with each digit being worth two times more than the last. Counting in Binary In binary, the first digit is worth 1 in decimal. The second digit is worth 2, the third worth 4, the fourth worth 8, and so on—doubling each time. Adding these all up gives you the number in decimal. So, 1111 (in binary)Â =Â 8 + 4 + 2 + 1Â =Â 15 (in decimal) Accounting for 0, this gives us 16 possible values for four binary bits. Move to 8 bits, and you have 256 possible values. This takes up a lot more space to represent, as four digits in decimal give us 10,000 possible values. It may seem like we’re going through all this trouble of reinventing our counting system just to make it clunkier, but computers understand binary much better than they understand dec...

As Numbers are not only the mere symbols on a page but there is much more significance of numbers. In the study of mathematics, numerous number systems exist, each with its own significance and applications. From the familiar decimal system we use daily to the intriguing worlds of binary, octal, and hexadecimal, these systems offer unique perspectives on numerical representation. In this article, we explore the concepts of number systems and also learn about these different number system types. The number system includes different types of Numbers Definition Numbers are used in various arithmetic values applicable to carry out various arithmetic operations like addition, subtraction, multiplication, etc which are applicable in daily lives for the purpose of calculation. Numbers are the mathematical values or figures used for the purpose of measuring or calculating quantities. It is represented by numerals as 2, 4, 7, etc. Some examples of numbers are integers, whole numbers, natural numbers, rational and irrational numbers, etc. The value of a number is determined by the digit, its place value in the number, and the base of the number system. Numbers generally also known as numerals are the mathematical values used for counting, measurements, labeling, and measuring fundamental quantities. What is a Number System? A Number system or numeral system is defined as an elementary system to express numbers and figures. It is the unique way of representing of numbers in arithmeti...

A number is a mathematical object used to count, label, and measure. A number system is a systematic way to represent numbers. The number system we use in our day-to-day life is the decimal number system that uses 10 symbols or digits. The number 289 is pronounced as two hundred and eighty-nine and it consists of the symbols 2, 8, and 9. Similarly, there are other number systems. Each has its own symbols and method for constructing a number. ASCII The code called ASCII (pronounced ‘􀀏’.S-key”), which stands for American Standard Code for Information Interchange, uses 7 bits to represent each character in computer memory. The ASCII representation has been adopted as a standard by the U.S. government and is widely accepted. A unique integer number is assigned to each character. This number called ASCII code of that character is converted into binary for storing in memory. For example, the ASCII code of A is 65, its binary equivalent in 7-bit is 1000001. Since there are exactly 128 unique combinations of 7 bits, this 7-bit code can represent only128 characters. Another version is ASCII-8, also called extended ASCII, which uses 8 bits for each character, can represent 256 different characters. For example, the letter A is represented by 01000001, B by 01000010 and so on. ASCII code is enough to represent all of the standard keyboard characters. EBCDIC It stands for Extended Binary Coded Decimal Interchange Code. This is similar to ASCII and is an 8 bit code used in computers ma...

Electronic and Digital systems may use a variety of different number systems, (e.g. Decimal, Hexadecimal, Octal, Binary), or even Duodecimal or less well known but better named Uncial. All the other bases other than Decimal result from computer usage. Uncial (named from Latin for 1/12 “uncia” the base twelve analogue of Decimal from the Latin word for 1/10 “decima”). A number N in base or radix b can be written as: 2. Binary to Decimal (1010.01) 2 1x2 3 + 0x2 2 + 1x2 1+ 0x2 0 + 0x2 -1 + 1x2 -2 = 8+0+2+0+0+0.25 = 10.25 (1010.01) 2 = (10.25) 10 3. Decimal to Octal (10.25) 10 (10) 10 = (12) 8 Fractional part: 0.25 x 8 = 2.00 Note: Keep multiplying the fractional part with 8 until decimal part .00 is obtained. (.25) 10 = (.2) 8 Answer: (10.25) 10 = (12.2) 8 4. Octal to Decimal (12.2) 8 1 x 8 1 + 2 x 8 0 +2 x 8 -1 = 8+2+0.25 = 10.25 (12.2) 8 = (10.25) 10 5. Hexadecimal to Binary To convert from Hexadecimal to Binary, write the 4-bit binary equivalent of hexadecimal. (3A) 16 = (00111010) 2 6. Binary to Hexadecimal To convert from Binary to Hexadecimal, start grouping the bits in groups of 4 from the right-end and write the equivalent hexadecimal for the 4-bit binary. Add extra 0’s on the left to adjust the groups. 1111011011 0011 1101 1011 (001111011011 ) 2 = (3DB) 16 7. Binary to Octal To convert from binary to octal, start grouping the bits in groups of 3 from the right end and write the equivalent octal for the 3-bit binary. Add 0’s on the left to adjust the groups. Example: