In computers we normally use four different numbering systems - Decimal, Binary, Octal and Hexadecimal.The decimal system is a number system which is used in our day-to-day transactions like currency,counting etc. In this system,the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are used to denote various numbers.In Binary number system, 0's (zeros) and 1's (ones) are the only symbols that are used to represent numbers of all magnitudes (sizes). For example, a normal decimal number 3 (three) is represented in a binary as 11. We shall learn more about it in the later sections.Binary system is mostly used in computers and other computing devices.A number in a particular base is written as (Number)base of number. For example (34)10 is a decimal number (Thirty Four) and (11)2 is a binary number 11 (it is read as One One and not as Eleven) which actually represents a decimal number whose value is 3.Since the decimal number system is more commonly used,the decimal number (124)10 is simply written as 124. However, if the same number has to be represented in binary system, it is written as (1111100)2.Similarly, the octal number system uses 8 as its base. It is generally used in digital displays and in representing file permissions under UNIX/Linux operating systems.Hexadecimal system or Hex is a number system that uses 16 as the base to represent numbers. We shall learn more about octal and hexadecimal number systems in the later sections.Select the correct statements from the given statements.A number system that uses only two digits, 0 and 1 is called Binary number system.The ten digits used in the decimal number system are from 1 to 10.The two symbols 0 and 1 are known as bits in a binary system.The base of an octal system is 8.Close

The binary number system is used both in mathematics and digital electronics.The binary number system or base-2 numeral system represents numeric values using only two symbols - 0 (zero) and 1 (one).Computers have circuits (logic gates) which can be in either of the two states: off or on. These two states are represented by 0 (zero) and 1 (one) respectively .It is for this reason that computation in systems is performed using a binary number system (base-2) where all numbers are represented using 0's and 1's.Each binary digit, i.e.,0 (zero) or 1 (one) is called a bit (binary digit). A collection of 8 such bits is called a Byte.In computer terminology, different names have been given to multiples of 210 (i.e., 1024 times existing value), as shown in the table given below:1 byte = 8 bits1 kilobyte = 1024 bytes1 megabyte = 1024 kilobytes1 gigabyte = 1024 megabytes1 terabyte = 1024 gigabytes1 petabyte = 1024 terabytesIn a computer, text, images, music, videos or any type of data for that matter is eventually stored in binary format on the disk.Select the correct statements from the given statements.In binary system the base is 2.A byte is composed of 10 bits.1MB (megabyte) = 8388608 bits.A decimal number cannot be represented as a binary number.

Why do electronic computers represent numbers using the binary system rather than the decimal system?

The numbering system which uses base-8 is called octal system. A base (also called radix) is the number of unique digits or symbols (including 0) that are used to represent a given number.In octal system (or the base-8 system), a total of 8 digits (0, 1, 2, 3, 4, 5, 6 and 7) are used to represent a number of any size (magnitude).For example, Zero is represented as 0, where0 = (0 * 80) = (0 * 1)Similarly the numbers 1 One (1), 2 and 7 are represented as follows: :1 = (1 * 80) = (1 * 1)2 = (2 * 80) = (2 * 1)...7 = (7 * 80) = (7 * 1)Now, let us try to represent the following numbers in octal system:Eighteen (18): Since 0 to 7 are the only digits that can be used to represent 18, let us divide 18 by 8 and write the quotient and remainder as follows:[quotient][remainder], i.e.: [2][2]18 = (2 * 81) + (2 * 80) = (16) + (2)Four Hundred and Twenty One (421): Since 0 to 7 are the only digits that can be used to represent 421,, let us divide it by 8 and write the quotient and remainder as follows:[quotient][remainder], i.e.: [52] [5] (further dividing 52 by 8 we get [6][4]), which is [6][4][5]421 = (6 * 82) + (4 * 81) + (5 * 80) = (384) + (32) + (5)Click on Live Demo to understand the conversion of decimal number system to octal number system.In order to differentiate from decimal numbers, octal numerals are prefixed with a leading 0 (zero).For example, to store an octal value of seven into a variable number_seven, we writeint number_seven = 07;Similarly, if we want to store an octal representation of a decimal number 9 in a variable number_nine, we writeint number_nine = 011;Click on Live Demo to understand the conversion of octal number system to decimal number system.Select all the correct statements from the given statements.In octal system, the base is 10.In octal system, decimal value of 20 is represented as 21In octal system, decimal 8 is represented as 10In octal system, decimal of 10 is written as 012

he numbering system which uses base-2 is called the binary system. In binary system (or the base-2 system), a total of 2 digits (0 and 1) are used to represent a number of any size (magnitude).For example, Zero is represented as 0, where0 = (0 * 20) = (0 * 1)Similarly, One (1) is represented as:1 = (1 * 20) = (1 * 1)Now, let us try to represent the following numbers in binary format:Two (2): Since 0 or 1 are the only digits that can be used to represent 2, let us divide 2 by 2 and write the quotient and remainder as follows:[quotient][remainder], i.e.: [1][0]2 = (1 * 21) + (0 * 20) = (2) + (0)Three (3): Since 0 or 1 are the only digits that can be used to represent 3, let us divide 3 by 2 and write the quotient and remainder as follows:[quotient][remainder], i.e.: [1][1]3 = (1 * 21) + (1 * 20) = (2) + (1)Four (4): Since 0 and 1 can be only be used to represent 4, let us divide 4 by 2 and write the quotient and remainder as follows:[quotient][remainder], i.e.: [2][0]. By repeating the above logic for 2 (whose value we already know to be [1][0]) we get [1][0][0]4 = (1 * 22) + (0 * 21) + (0 * 20)4 =      (4)     +     (0)      +     (0)Fourteen (14): Since only 0 and 1 should be used, let us divide 14 by 2 and write the quotient and remainder as follows:[quotient][remainder], i.e.: [7][0], by repeating the above logic for 7 (7 = [3][1], and 3 = [1][1]) we finally get [1][1][1][0]14 = (1 * 23) + (1 * 22) + (1 * 21) + (0 * 20)14 =       (8)     +     (4)     +     (2)     +     (0)Hundred and Fourteen (114): let us divide 114 by 2 and write the quotient and remainder as follows:[quotient][remainder], i.e.: [57][0], by repeating the above logic for 57 (57 = [28][1], 28 = [14][0], 14 = [1][1][1][0]), we finally get [1][1][1][0][0][1][0]114 = (1 * 26) +(1 * 25) +(1 * 24) +(0 * 23) + (0 * 22) + (1 * 21) + (0 * 20)114 =     (64)    +    (32)    +    (16)    +    (0)     +      (0)     +     (2)     +      (0)Click on Live Demo to understand the conversion of decimal number system to binary number system.In C, binary numerals are prefixed with a leading 0b (or 0B) (digit zero followed by char 'b'). For example, to store an binary value of four into a variable binary_four, we writeint binary_four = 0b100;Click on Live Demo to understand the conversion of binary number system to decimal number system.Select the correct statements from the given statements.In binary system, decimal 10 is represented as (1 * 101)In binary system, decimal 100 = binary 1100100In binary system, decimal 10 = binary 1010In binary system, decimal 200 = binary 100100

The number system which uses base-16 is called hexadecimal system (or simply hex).In binary system (or base-2 number system), a total of 2 digits (0 and 1) are used to represent a number of any size (magnitude) and in octal system (or base-8 number system), a total of 8 digits (0 to 7) are used.Similarly in hexadecimal system (or base-16 number system), a total of 16 characters (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F) are used to represent a number of any size (magnitude).The highest digit in hex is (F)16. The number (F)16 in binary is represented as (1111)2. Here, four binary digits (bits) are used to represent the highest hexadecimal digit.In hex to binary conversion,four bits are used to represent each hex digit.The following table shows the conversion of each hex digit into its corresponding binary digits.Hexadecimal 0 1 2 3 4 5 6 7 8 9 A B C D E FBinary 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111For example, hexadecimal number 0x5AF6 is converted into its corresponding binary form as follows:Hex Number -> 5 A F 6Binary Number -> 0101 1010 1111 0110Hence, 0x5AF6 is (0101101011110110)2Click on Live Demo to understand the conversion of a hexadecimal number into its corresponding binary form.Similarly while converting a binary number into a hex number, the binary number is first divided into groups of 4 digits each, starting from the extreme right side. Each of the four binary digits are replaced with their corresponding octal digits.If the group to the extreme left side of binary digits does not have four digits, the required number of zeros are added as a prefix to make a group of four binary digits.For example, let us try convert the following binary 1101100 number into hex.Binary Number -> 110 1100Binary Number -> 0110 1100 // After prefixing zeros in the left most groupHexadecimal Number -> 6 CHence, the hex equivalent of the given binary 1101100 is 0x6CClick on Live Demo to understand the conversion of the binary number into its corresponding hexadecimal form.Select all the correct statements from the given statements.(F3G9)16 is a hexadecimal number.Each hexadecimal digit is represented as three bit binary number.Binary number (10101110)2 is equal to the hexadecimal number (AE)16.Hexadecimal number (369)16 is equivalent of binary number (1101101001)2.