Number System In Computers

The Roman Number System is not a positional number system because it does not rely on the position of digits to determine their value. Instead, it uses a combination of letters to represent numbers. In a positional number system, such as octal, binary, or hexadecimal, the value of a digit is determined by its position in the number.

In a number system, each position of a digit represents a specific power of the base. This means that the value of a digit in a number is determined by its position and the base of the number system. For example, in the decimal system, the value of the digit in the units place is multiplied by 10^0, the value of the digit in the tens place is multiplied by 10^1, and so on. This concept applies to other number systems as well, such as binary, octal, and hexadecimal. Therefore, the statement is true.

In computer terminology, a bit is the smallest unit of data and represents a binary digit. It can have a value of either 0 or 1. These binary values are the foundation of all data processing in computers, where combinations of bits are used to represent more complex data, such as numbers, letters, or instructions. Therefore, the statement that a bit means either 0 or 1 is true.

The value of radix in the binary number system is 2. The radix represents the base or the number of unique digits used in a number system. In the binary system, only two digits, 0 and 1, are used to represent numbers. Therefore, the radix in the binary system is 2.

The binary equivalent of a decimal number is obtained by repeatedly dividing the decimal number by 2 and noting the remainders. The remainders, when read from bottom to top, give the binary equivalent. In this case, dividing 10 by 2 gives a quotient of 5 and a remainder of 0. Dividing 5 by 2 gives a quotient of 2 and a remainder of 1. Dividing 2 by 2 gives a quotient of 1 and a remainder of 0. Dividing 1 by 2 gives a quotient of 0 and a remainder of 1. Reading the remainders from bottom to top gives the binary equivalent 1010.

Computers operate using the binary number system because it aligns with the on/off states of electronic switches (transistors) that form the foundation of their hardware. Each digit in a binary number is called a bit, and a group of eight bits forms a byte. The binary system provides a simple and efficient way to represent data and instructions within a computer.

The correct representation of a binary number is a sequence of 0s and 1s. In this case, option d) (000)2 is the correct answer as it represents a binary number with three digits, all of which are 0.

In an octal number system, the digits range from 0 to 7. Therefore, the maximum value of a single digit in an octal number system is 7.

The binary number 111 represents the decimal number 7. In octal format, each digit represents three binary digits. Therefore, the binary number 111 can be split into three digits: 1, 1, and 1. Each digit can then be converted to its octal equivalent, which is 1. Combining the three octal digits gives the octal number 111, which is equivalent to the decimal number 7.

To represent an octal number in binary, we need to convert each octal digit to its binary equivalent. Since each octal digit can be represented by 3 bits in binary (as there are 8 possible combinations of 3 bits), the maximum number of bits required to represent an octal number is 3. Therefore, the correct answer is b) 3.