Chapter:15 | Concept of Number System

 

Chapter|15 Concept of Number System

 Concept of Number System

Write very short answer of the following questions:

a. Which country used the finger numerals system early days?

Ans: The finger numeral system was used by various cultures, and its early use cannot be attributed to a specific country.

b. When did Hindus developed decimal number system?

Ans: About in the fifth century, Hindus developed decimal number system.

c. Is octal number system has base 8?

Ans: Yes octal number system has base 8.

d. How many letters are used in Hexadecimal number system?

Ans: The hexadecimal number system uses 16 different symbols, including the numbers 0-9 and the letters A-F.

e. Can we divide binary numbers?

Ans: Yes we can divide binary numbers.

f. How many bits make a byte?

Ans: Eight bits make a byte.

Write short answer of the following questions:

a. What is number system?

Ans: A number system is the set of symbols used to express quantities as the basis for counting, determining order, comparing amounts, performing calculations, and representing value.

b. How did early people calculate?

Ans: Earlier, people used their fingers, pebbles, or sticks for counting and performed simple calculations such as addition of numbers, subtraction, etc.

c. What is decimal number system?

Ans: The decimal number system is the most common number system that we use in our daily life. It uses ten digits 0-9 so it has base 10.

d. What is octal number system? What is its base value.

Ans: The octal number system uses 8 digits (0-7) and has a base value of 8.

e. What is binary number system? Which digits are used in this system?

Ans: The binary number system is a system that uses only two digits: 0 and 1.

f. What is hexadecimal number system? Why it has base sixteen?

Ans: The hexadecimal number system is a base-16 number system. It uses 16 different digits, which are 0-9 followed by A, B, C, D, E, and F.

Write long answer of the following questions:

a. Explain different types of number system with their examples.

Ans: There are several types of number systems, each with its own base and set of digits. Here are some of the most common ones along with examples:

a. Decimal number system

The decimal number system is the most common number system that we use in our daily life. It uses ten digits 0-9 so it has base 10. Example = 135

 b. Binary number

The binary number system is a system that uses only two digits: 0 and 1.

Example: 1101 (in binary) = 13 (in decimal)

c. Octal number system

The octal number system uses 8 digits (0-7) and has a base value of 8.

Example: 75 (in octal) = 61 (in decimal)

d. Hexadecimal number system

The hexadecimal number system is a base-16 number system. It uses 16 different digits, which are 0-9 followed by A, B, C, D, E, and F.

Example: 1A3 (in hexadecimal) = 419 (in decimal)

b. Write the steps to convert decimal number to binary number and vice versa.

Ans: Follow these steps to convert a decimal to binary number system.

1. Divide the given decimal number by 2 and write down the reminders in one column

2. Then divide the quotient by 2 and again write down the reminders.

3. Continue the process until the quotient is zero. And at the same time write down the remainder values respectively.

4. Write all the remainders tarting with the most significant digit i.e. from bottom to top.

Now you will get equivalent binary number of the given decimal number.