Exercises
1. Choose the correct option.
i. What is the result of the binary addition: 1101 + 1011?
a. (11010)2 b. (11000)2 c. (11110)2 d. (11101)2
ii. When adding two binary numbers, what is the carrying value in binary addition?
a. 100 b. 1 c. 10 d. 11
iii. In binary multiplication, what is the result when multiplying any binary digit by 0?
a. 1 b. 11 c. 0 d. The original digit
iv. What is the base of the octal number system?
a. 2 b. 7 c. 8 d. 10
v.What is binary equivalent to the octal number 64?
a. (110100)2 b. (1101111)2 c. (1110001)2 d. (11000101)2
vi. In the hexadecimal system, what does the symbol 'A' represent?
a. 11 b. 12 c. 10 d. 13
2. Answer these questions.
a) What is a number system?
Ans: A number system is a method of representing numbers using different symbols or digits. It helps us write and perform calculations with numbers in mathematics and computers.
b) Define the base or radix of the number system.
Ans: The base or radix of a number system is the total number of unique digits or symbols used in that number system.
For example:
Decimal system has base 10 because it uses 10 digits (0–9).
Binary system has base 2 because it uses 2 digits (0 and 1).
c) List out the different types of number systems.
Ans: The main types of number systems are:
i) Binary Number System (Base 2)
ii) Octal Number System (Base 8)
iii) Decimal Number System (Base 10)
iv) Hexadecimal Number System (Base 16)
d) What is a hexadecimal number system? Write down the symbols used in the hexadecimal number system.
Ans: The hexadecimal number system is a number system with base 16. It is commonly used in computers and digital electronics.
It uses the following symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
Here: A = 10 , B = 11 ,C = 12 , D = 13 , E = 14 ,F = 15
3. Calculate the following as indicated:
a. Perform the following binary addition:
i. (11110)2 +(1001)2
ii. (1011)2 +(1001)2
iii. (101011)2 +(11011)2
iv. (1010)2 +(110)2
v. (101001)2 +(1110)2
vi. (100001)2 +(100011)2
vii. (100111)2 +(11010)2
viii. (110001)2 +(100101)2
b. Perform the following binary subtraction:
i. (1100)2
- (1001)2
ii. (1001)2
- (110)2
iii. (11101)2
- (1010)2
iv. (101100)2
- (10011)2
v. (11111)2
- (10110)2
vi. (110011)2
- (10100)2
vii. (100100)2
- (1110)2
viii. (1000001)2
- (10101)2
