## Chapter 1 Number System

Brain Developers

A. Fill in the blanks:

1. The base of Binary number system is __2__.

2. The base of __decimal__ number system is 10.

3. Octal number system consists of __8__ digits.

4. In Binary addition, 1 + 1 equals to __10__.

5. __Binary__ number system is understood by the computer system.

6. __Hexadecimal__ number system uses 16 digits, from 0 to 9 and letters A to F.

7. In Binary subtraction, 1 - 1 equals to __0__.

B. State True or False:

1. You cannot perform arithmetical operations on binary numbers. (False)

Correct Answer: You can perform arithmetical operations on binary numbers.

2. The decimal number system consists of 10 digits, i.e., 0 to 9. (True)

3. The method to perform division of two binary numbers is not the same as that of decimal numbers. (False)

Correct Answer: The method to perform division of two binary numbers is the same as that of decimal numbers.

4. 1 multiplied by 0 equals to 0. (True)

5. Charles Babbage introduced the concept of 0 (Zero). (False)

Correct Answer: Aryabhat introduced the concept of 0 (Zero).

6. The numbers used in Octal number system are 1 to 7. (False)

Correct Answer: The numbers used in Octal number system are 0 to 7.

C. Application Based Questions:

1. Ratika's computer teacher asked her to convert the Octal number to Decimal number. Suggest her the method which she should apply in converting the Octal number.

Answer: Multiply each octal number with 8 having the power 0 for unitary position, starting from the extreme right digit.

2. The teacher has given as assignment to Saurabh on Binary subtraction. Saurabh is confused how to subtract 1 from 0. Help him solving the problem.

Answer: He can solve this by borrow method as (0 - 1 = 1).

D. Multiple Choice Questions:

1. _____________ introduced the concept of 0 (Zero).

a) Ada Lovelace

b) Aryabhat

c) Charles Babbage

Answer: b) Aryabhat

2. A __________ converts the decimal format into its binary equivalent.

a) Digital Computer

b) Cell Phone

c) Abacus

Answer: a) Digital Computer

3. A computer understands only the ___________ code.

a) English

b) French

c) Binary

Answer: c) Binary

4. In Binary multiplication, 1 × 1 equals to ____________.

a) 0

b) 1

c) 2

Answer: b) 1

5. To convert a Decimal number into a Binary number, divide the number by _____________.

a) 2

b) 8

c) 10

Answer: a) 2

E. Answer the following:

1. What is a number system? Explain its commonly used types.

Answer: There are four different types of number system -

a) Binary number system

b) Octal number system

c) Decimal number system

d) Hexadecimal number system

2. What are the rules to convert a Decimal number into a Binary number?

Answer:

Step 1: Divide the given decimal number with the base 2.

Step 2: Write down the remainder and divide the quotient again.

Step 3: Repeat the step 2 until the quotient is 0.

3. Write the rules to multiply two Binary numbers.

Answer: The rule for performing multiplication using binary numbers is the same that of the numbers. 0 × 0 = 0, 0 × 1 = 0, 1 × 0 = 0 & 1 × 1 = 1.

4. Briefly explain the Octal number system.

Answer: Octal number system consists of 8 digits i.e. 0 to 7 with the base 8.

5. What do you understand by the Hexadecimal number system?

Answer: Hexadecimal number system contains 16 digits, and therefore, has the base 16. It uses the digits (0 - 9) and (A - F).

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