The computer data is represented using the binary system. Binary system is a number system that uses 0s and 1s to represent and store the data. The smallest unit of data in binary system is a digit or bit and is represented as 0 or 1. Computer processor is a circuit made up of a number of transistors. Each transistor contains a tiny switch that activates when the electronic signal is received. The digit 0 represents the off state and 1 represents the on state of a transistor. Computer programs can be described as the set of instructions, and each instruction is translated into the machine code to activate the CPU. A computer code is written by the programmer, and the translator converts this code into binary instructions

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It is referred as the base 8 number system as it consists of eight digits from 0 to 7. In an octal number system, position of each digit represents power of 8. As this system consists of eight digits only, eah digit is always represented by one of the 0 to 7 digits only. The Octal number system is equivalent of binary number and is used as a shorthand representation for the long binary numbers. Octal is also used as shorthand for the UNIX file permissions. For instance file mode rwxr-xr-x can be represented as 0755. Octal number system is also used when a word contains a number of bits that is divisible by 3. For example, ancient systems that contain 18 bit word size or systems that have 9 bit bytes.

Role of Decimal in Computing:

Decimal number system is used in day to day life as it contains decimal number that has a base 10 and it uses digits from 0 to 9. In this system the successive positions to the left represents units, tens, hundreds, thousands and so on. Each position shows the specific power of base 10. Earlier computers were designed using the decimal number system, but this created unnecessary complexities and did not make good use of computers.

Role of Hexadecimal in

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The most common example in computers for using base greater than 16 is the computer memory address. The first microcontrollers used only a 4 bit address. As the need for more processing power increased, the need to increase the byte size in the controller was inevitable. As the bit size keeps increasing so does the representation of numbers from a lower base to a higher base. We moved from binary representation to hexadecimal representation as it would be easier to store and compute. Similarly, moving to a base greater than 16 will make it easier on computation as our processors get complicated by the day. Ultimately it boils down to grouping a large number of binary combinations into a small set of numbers as the base increases. This makes the coding and computation compact and