2.1 Concept of Number System 

Number System is a writting system with specific symbols and rules for expressing numbers and doing different calculations.

Decimal: base-10 (0-9)

Binary: base-2 (0,1)

Octal: base-8 (0-7)

Hexa: base-16 (0-9,A-F)

a) What is a digit? What is a computer word?

Digit: A single symbol used to count or represent numbers (like 0–9 in decimal, or 0 and 1 in binary).

Computer word: The fixed number of bits (such as 16, 32, or 64 bits) that a computer's CPU can process as a single unit at one time.

b) Define the base or radix of the number system.

The total number of unique digits or symbols available in a specific number system (for example, base 10 for decimal, base 2 for binary).

c) Which language is used by computer systems, smartphones, and tablets?

Machine language (Binary code consisting of 0s and 1s).

Application of number system conversion app

  • Human-computer interactions 
  • Colour code in html
  • Networking IP and MAC
2.2 Binary Calculations 

Binary addition: 0+0=0  0+1=1  1+0=0  1+1=0 cary 1

Binary subtraction: 0-0=0 1-0=1 1-1=0 0-1=1 borrow 1

2.3 Number Conversion 


Decimal to binary, octal, hexadecimal 

Divide given decimal number by obtained conversion base number until quotient 0.

Binary, octal, hexadecimal to decimal 

Multiply given conversion base with it's radix.

Binary ⇋ hexadecimal 

Binary in four digits groups from right to left respective hexadecimal.

Ex

1. Choose the Correct Option

i. What is the result of the binary addition: 1101 + 1011?

Ans:c. (11000)

ii. When adding two binary numbers, what is the carrying value in binary addition?

 Ans:b. 1

 iii. In binary multiplication, what is the result when multiplying any binary digit by 0?

Ans: c. 0

iv. What is the base of the octal number system?

   Ans:c. 8

v. What is binary equivalent to the octal number 64?

Ans: a. (110100) *(Since 6 = 110 and 4 = 100)

 vi. In the hexadecimal system, what does the symbol 'A' represent?

 Ans:c. 10

2. Answer These Questions

a) What is a number system?

Ans:A number system is a writing system with specific symbols and rules used for expressing numbers and performing calculations.

b) Define the base or radix of the number system.

Ans:The base or radix is the total number of unique digits or symbols used to represent values in that specific number system.

 c) List out the different types of number systems.

  Ans:Decimal, Binary, Octal, and Hexadecimal number systems.

d) What is a hexadecimal number system? Write down the symbols used in the hexadecimal number system.

Ans:It is a base-16 number system that uses sixteen distinct alphanumeric symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F.

3. Calculate the Following as Indicated

a. Perform the following binary addition:

i. (11110)+ (1001) = (100111)

ii. (1011) + (1001)= (10100)

iii. (101011) + (11011) = (1000110)

iv. (1010) + (110) = (10000)

v. (101001)+ (1110)= (110111)

vi. (100001) + (100011)= (1000100)

vii. (100111)+ (11010)= (1000001)

viii. (110001)+ (100101) = (1010110)

b. Perform the following binary subtraction:

i. (1100) - (1001) = (11)

ii. (1001) - (110) = (11)

iii. (11101) - (1010) = (10011)

iv. (101100) - (10011) = (11001)

v. (11111) - (10110) = (1101)

vi. (110011) - (10100) = (100011)

vii. (100100) - (1110) = (10110)

viii. (1000001) - (10101) = (101100)

4. Convert the Given Numbers as Indicated

a. Decimal to Binary Conversion

i. (56) = (111000)

ii. (78) = (1001110)

iii. (123) = (1111011)

 iv. (345) = (101011001)

v. (540) = (1000011100)

vi. (572) = (1000111100)

vii. (546) = (1000100010)

viii. (1098) = (10001001010)

ix. (2103) = (100000110111)

x. (445) = (110111101)

 b. Binary to Decimal Conversion

 i. (1101) = (13)

 ii. (1010) = (10)

 iii. (10010) = (18)

 iv. (10110) = (22)

 v. (101001) = (41)

 vi. (11100111) = (231)

 vii. (111100) = (60)

 viii. (10010011) = (147)

ix. (1011100) = (92)

 x. (100110) = (38)

Convert the Given Numbers as Indicated

c. Decimal to Octal Conversion

 i. (69) = (105)

 ii. (216) = (330)

 iii. (767) = (1377)

 iv. (79) = (117)

 v. (443) = (673)

 vi. (413) = (635)

 vii. (765) = (1375)

 viii. (1334) = (2466)

 ix. (1825) = (3441)

 x. (2783) = (5337)

d. Octal to Decimal Conversion

 i. (124) = (84)

ii. (242) = (162)

iii. (333) = (219)

iv. (763) = (499)

v. (103) = (67)

vi. (451) = (297)

vii. (3401) = (1793)

viii. (1045) = (549)

 ix. (437) = (287) Let 8 as 7

x. (611) = (393)

e. Decimal to Hexadecimal 

 i. (55) = (37)

ii. (540) = (21C)

iii. (225) = (E1)

iv. (880) = (370)

 v. (2046) = (7FE)

 vi. (2024) = (7E8)

 vii. (6678) = (1A16)

 f. Hexadecimal to Decimal Conversion

i. (56) = (86)

ii. (67) = (103)

iii. (558) = (1368)

iv. (B74) = (2932)

v. (20\text{D}3) = (8403)

vi. (DEF) = (3567)

vii. (6E3) = (1763)

viii. (63F) = (1599)

g. Binary to Hexadecimal Conversion

i. (1000110) = (46)

ii. (11001) = (19)

iii. (1111000) = (78)

iv. (11110000111) = (787)

v. (101010110) = (156)

vi. (1110010110) = (396)

vii. (11011001) = (D9)

viii. (1001100) = (4C)

h. Hexadecimal to Binary Conversion

i. (D4) = (11010100)

ii. (643) = (011001000011) or (11001000011)

iii. (189) = (000110001001) or (110001001)

 iv. (2BF) = (001010111111) or (1010111111)

v. (A9F) = (101010011111)

 vi. (FACE})= (1111101011001110)

 vii. (FB4)= (111110110100)

 viii. (1B2) = (000110110010) or (110110010)


Practical Task

a. Demonstrate Calculation based on various numbers system mechanisms using  suitable conversion tools (e.g. online tool or Number System Convertion Mobile app).


Activities 

• Demonstrate the manual conversion process hands-on.

• Visual charts help students learn and convert number systems.

• Student engagement and peer evaluation must be applied.

• Use online tool conversion calculators for decimal, binary, octal, and hexadecimal numbers.