• Class: Eight

Chapter 1: Number System

Exercise Solution

1. Fill in the blanks:

a) Codes in the form of combination of 0's and 1's known as
ASCII.
b) The arithmetic that uses 0 and 1 is called
Binary Number System.
c) A computer does processing on the basis of two digits i.e. 0  and 1 .
d) Complement means interchange of bits.

2. Convert the following decimal numbers into their equivalent binary numbers:

a) 85                                                         b) 103 (85)10 = (1010101) (103)10 = (1100111)2 c) 256                                                        d) 13 (256)10 = (100000000) (13)10 = (1101)2

3. Convert the following binary numbers into their equivalent decimal numbers:

a) 10101

Solution:

(10101)= 1x24 + 0x23 + 1x22 + 0x21 + 1x20

1x16 + 0x8 + 1x4 + 0x2 + 1x1

= 16 + 0 + 4 + 0 + 1

= (21)10

b) 10010

Solution:

(10101)= 1x24 + 0x23 + 0x22 + 1x21 + 0x20

1x16 + 0x8 + 0x4 + 1x2 + 0x1

= 16 + 0 + 0 + 2 + 0

= (18)10

c) 11001

Solution:

(10101)= 1x24 + 1x23 + 0x22 + 0x21 + 1x20

1x16 + 1x8 + 0x4 + 0x2 + 1x1

= 16 + 8 + 0 + 0 + 1

= (25)10

d) 1000001

Solution:

(10101)= 1x26 + 0x25 + 0x24 + 0x23 + 0x22 + 0x21 + 1x20

1x64 + 0x32 + 0x16 + 0x8 + 0x4 + 0x2 + 1x1

= 64 + 0 + 0 + 0 + 0 + 0 + 1

= (65)10

4. Convert the following hexadecimal numbers into their equivalent decimal numbers:

a) 1AB

Solution:

(1AB)16 = 1x162 + Ax161 + Bx160

1x256 + 10x16 + 11x1

= 256 + 160 + 11

= (427)10

b) FF

Solution:

(FF)16 = Fx161 + Fx160

15x16 + 15x1

= 240 + 15

= (255)10

5. Compute the following binary arithmetic:

a) 10110 + 10110                                                b) 101010 + 100011

Solution:                                                              Solution:  So, 10110 + 10110 = 101100                                            So, 101010 + 100011 = 1001101

c) 111100 + 101101                                             d) 001101 + 101110

Solution:                                                               Solution:  So, 111100 + 101101 = 1101001                                     So, 001101 + 101110 = 111011

e) 1111000 - 1011100

Solution:

1111000 - 1011100 = 11100

f) 0100000 - 1011100

Solution:

0100000 - 1011100 = 111100

g) 1010111 - 1110101

Solution:

1010111 - 1110101 = 11110

h) 1010101 - 0101010

Solution:

1010101 - 0101010 = 101011

a) What is Binary Number System?

b) What do you mean by complement of bits?

c) What is "ASCII"?

d) What is base oR radix of a number?

e)  What is "Number System"?

7. Sunita has converted decimal number 53 to its binary equivalent but she is not sure whether it has been done correctly or not. How can she be sure that she has converted it correctly? Suggest the correct answer.

8. Lianna has a hobby of collecting stamps. She has collected many stamps whose binary equivalent is 101111 stamps. Can you find the number of stamps collected which can be understood by her father who does not know about binary number system?