Chapter 9| Basic Concept of Number System

 

Write full forms of the following:

a. Bit: Binary Digit

b. MSB: Most Significant Bit

c. LSD: Least Significant Digit

d. MSD: Most Significant Digit

Write very short answer of the following questions.

a. Which number system is used computer for processing?

Ans: The Binary number system is used by computers for processing.

 b. What is the base value of decimal number system?

Ans: The base value of the decimal number system is 10.

C. Who invented decimal digits?

Ans: The Hindu-Arabic numeral system, which forms the basis of decimal digits, was invented by Indian mathematicians and introduced to Europe through Arab mathematicians.

d. What do you understand by pebbles?

Ans: Pebbles were early tools used by people to perform counting or calculations in ancient times.

e. Does binary number system contain three digits?

Ans: No, the binary number system only contains two digits: 0 and 1.

Write short answer of the following questions:

a. How did early people used to calculate?

Ans: Early people used tools such as fingers, pebbles, and tally marks to perform basic calculations like counting and measuring.

b. What is a number system?

Ans: A number system is a mathematical way of expressing numbers using a set of symbols and rules. Different number systems use different base values, like binary (base 2), decimal (base 10), octal (base 8), and hexadecimal (base 16).

C. Write basic rules in number system.

Ans:  The basic rules in number system are:

Any number to the O^th of power equals to 1.

Any number to the 1^st of power equals to the same number (number itself).

Any number can be represented as powers of the system's base.

The number system of base n requires n number of digits.

Digits of a number are counted from right to left and the right most digits is the first digit of that number.

Most Significant Bit (MSB) is the left most bit of a binary value.

Least Significant Bit (LSB) is the right most bit of a binary value.

 

d. What are the different types of number systems?

Ans: The different types of number systems are:

·        Binary (Base 2): Uses digits 0 and 1.

·        Decimal (Base 10): Uses digits 0 to 9.

·        Octal (Base 8): Uses digits 0 to 7.

·        Hexadecimal (Base 16): Uses digits 0 to 9 and letters A to F.

e. What is decimal number system? Write the digits used by decimal number system?

Ans: The decimal number system is a positional number system with a base of 10. It uses the digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

f. Write down steps to convert:

i. Binary to Decimal:

• ·        Start from the rightmost bit (LSB) and assign it a position starting from 0.
• ·        Multiply each bit by 2 raised to the power of its position.
• ·        Add the results to get the decimal value.
• ·        Example: Binary 1011 → (1×2³) + (0×2²) + (1×2¹) + (1×2⁰) = 8 + 0 + 2 + 1 = 11 in decimal.

ii. Decimal to Binary:

• ·        Divide the decimal number by 2.
• ·        Write down the remainder (0 or 1).
• ·        Continue dividing the quotient by 2, writing down the remainders, until the quotient is 0.
• ·        The binary number is the remainders read in reverse order.
• ·        Example: Decimal 11 → 11 ÷ 2 = 5 remainder 1 → 5 ÷ 2 = 2 remainder 1 → 2 ÷ 2 = 1 remainder 0 → 1 ÷ 2 = 0 remainder 1. So, 11 in decimal = 1011 in binary.