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.

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

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

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

In a base n number system, all numbers are written using only the digits {0,1,..,n−1}. For example, in the decimal (= base 10) number system that you are used to using, all numbers are written using the digits 0,1,..,9, whereas in the binary (= base 2) number system that your computer uses, all numbers are written using the digits 0 and 1 only.Write a function basenum(num, base) that takes as arguments num (a non-negative integer) and base (a non-negative integer not greater than 10), and returns True if all digits of num are strictly less than base and False otherwise (using lazy evaluation). Once again, expect to be tripped up by the first hidden test if you do not use lazy evaluation.For example:>>> basenum(12345, 2)False>>> basenum(12345, 8)True>>> basenum(10110, 2)True>>> basenum(9, 5)False

Explain how you would convert a decimal to a binary number. What is the significance of the resulting binary number in computer systems?