 # Number Representation

## The decimal number system is composed of 10 numerals or symbols. Deca means 10 that is why this system is called decimal system. The decimal system is also called the base-10 system, because it has 10 digits. The decimal system is also called the base-10 system, because it has 10 digits. The decimal system is a positional-value system in which the value of a digit depends on its position. The decimal number system is composed of 10 numerals or symbols. The decimal system is also called the base-10 system, because it has 10 digits. In binary number system there are only two symbols or possible digit values, 0 and 1. The binary system is also known as base-2 system. The base-2 system can be used to represent any quantity that can be represented in decimal or other number systems. Octal number system is a positional value system, wherein each octal digit has its own value or weight expressed as a power of 8. Octal number system contains groups of three binary digits can be used to represent each octal digit. In hexadecimal number system, the groups of four bits represent each base 16 digit. In hexadecimal system, the digits A to F are equivalent to the decimal values 10 to 15.

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• Q1

Convert the decimal number (0.62)10 to its equivalent fractional binary number.

Marks:2

The conversion of decimal number (0.62)10 to its binary equivalent is as follows: approximately

• Q2

Marks:2

Following are the rules for binary addition:

0 + 0 = 0

0 + 1 = 1

1 + 0 = 1

1 + 1 = 10 (0 with carry 1)

1 + 1 + 1 = 11 (1 with carry 1)

• Q3

Define Number System.

Marks:1

Number System is a system of naming or representing numbers, such as the decimal system or the binary system.

• Q4

What do you understand by Binary number system.

Marks:1

The binary number system(base 2) is composed of two unique symbols: 0 and 1.