Presentation on number system in digital Electronics

Slide 1: Title Slide: presentation on number system

• Title: Number Systems in Digital Electronics
• Subtitle: Understanding the Basics
• Presented by: [Your Name]
• Date: [Presentation Date]

Notes:

• Introduce yourself and set the context for the presentation.
• Mention the significance of number systems in the field of digital electronics.

Slide 2: Introduction (presentation on number system)

• Key Points:
  • Importance of number systems in digital electronics
  • Overview of common number systems

Notes:

• Importance: Number systems are crucial in digital electronics as they form the basis for data representation, storage, and manipulation. Understanding these systems is essential for designing and analyzing digital circuits.
• Overview: Briefly introduce the common number systems: Decimal, Binary, Octal, and Hexadecimal. Explain that these systems will be discussed in detail.

Slide 3: Decimal Number System (presentation on number system)

• Key Points:
  • Base 10
  • Digits: 0-9
  • Common in everyday life

Notes:

• Base 10: The decimal system is a base-10 system, meaning it uses ten distinct digits.
• Digits: Digits range from 0 to 9.
• Common Usage: It’s the standard system for denoting integer and non-integer numbers. Used universally in daily activities like counting, commerce, and measurement.
• Example: Explain how the number 345 is represented in decimal: 345=3×102+4×101+5×100345 = 3 \times 10^2 + 4 \times 10^1 + 5 \times 10^0345=3×102+4×101+5×100.

Slide 4: Binary Number System (presentation on number system)

• Key Points:
  • Base 2
  • Digits: 0, 1
  • Fundamental to digital systems

Notes:

• Base 2: The binary system is a base-2 system, using only two digits.
• Digits: Digits are 0 and 1.
• Digital Systems: All digital electronics and computer systems use binary because it’s simple and reliable for representing two states (on/off, true/false).
• Example: Explain how the number 1101 is represented in binary: 1101=1×23+1×22+0×21+1×201101 = 1 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^01101=1×23+1×22+0×21+1×20.

Slide 5: Octal Number System

• Key Points:
  • Base 8
  • Digits: 0-7
  • Used as a shorthand for binary

Notes:

• Base 8: The octal system is a base-8 system.
• Digits: Digits range from 0 to 7.
• Shorthand for Binary: Octal simplifies binary representation by grouping binary digits in sets of three. Each octal digit corresponds to a three-bit binary sequence.
• Example: Convert octal 745 to binary:
  • 7 in binary is 111
  • 4 in binary is 100
  • 5 in binary is 101
  • So, 745 (octal) = 111 100 101 (binary).

Slide 6: Hexadecimal Number System

• Key Points:
  • Base 16
  • Digits: 0-9, A-F
  • Compact representation of binary

Notes:

• Base 16: The hexadecimal system is a base-16 system.
• Digits: Digits range from 0 to 9 and letters A to F (where A=10, B=11, …, F=15).
• Binary Compactness: Hexadecimal provides a compact form of binary representation by grouping binary digits in sets of four. Each hex digit corresponds to a four-bit binary sequence.
• Example: Convert hex 2F3 to binary:
  • 2 in binary is 0010
  • F (15) in binary is 1111
  • 3 in binary is 0011
  • So, 2F3 (hex) = 0010 1111 0011 (binary).

Slide 7: Conversion Between Number Systems

• Key Points:
  • Binary to Decimal
  • Decimal to Binary
  • Binary to Hexadecimal
  • Hexadecimal to Binary

Notes:

• Binary to Decimal: Sum the products of each binary digit and its corresponding power of 2. Example: 10112=1×23+0×22+1×21+1×20=11101011_2 = 1 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 = 11_{10}10112=1×23+0×22+1×21+1×20=1110.
• Decimal to Binary: Divide the decimal number by 2 and record the remainders. Example: Convert 13 to binary:
  • 13 ÷ 2 = 6 R1
  • 6 ÷ 2 = 3 R0
  • 3 ÷ 2 = 1 R1
  • 1 ÷ 2 = 0 R1
  • Read remainders bottom to top: 1101.
• Binary to Hexadecimal: Group binary digits in sets of four from right to left, then convert each group. Example: 110101112=1101201112=D71611010111_2 = 1101_2 0111_2 = D7_{16}110101112=1101201112=D716.
• Hexadecimal to Binary: Convert each hex digit to its four-bit binary equivalent. Example: 3A516=0011210102010123A5_{16} = 0011_2 1010_2 0101_23A516=001121010201012.

Slide 8: Arithmetic Operations in Different Bases

• Key Points:
  • Addition, Subtraction, Multiplication, Division
  • Binary arithmetic

Notes:

• Addition: Similar to decimal addition, but carries occur at base 2. Example:
  • 1011+11011011 + 11011011+1101
  • 1+1=10 (write 0, carry 1)
  • 1+0+1=10 (write 0, carry 1)
  • 1+1+1=11 (write 1, carry 1)
  • 1+1=10 (write 0, carry 1)
  • Result: 110001100011000.
• Subtraction: Use borrowing similar to decimal subtraction. Example:
  • 1011−01101011 – 01101011−0110
  • 1-0=1
  • 1-1=0
  • 0-1 (borrow) becomes 10-1=1, borrow from next digit.
  • Result: 010101010101.
• Multiplication: Similar to decimal multiplication but in base 2. Example: 101×11101 \times 11101×11:
  • 101
  • 1010 (shifted left)
  • Result: 111111111111.
• Division: Similar to decimal division but in base 2. Example: 1101÷101101 \div 101101÷10:
  • Perform bit by bit division.
  • Result: Quotient: 110110110, Remainder: 111.

Slide 9: Applications of Number Systems

• Key Points:
  • Digital circuits
  • Computer programming
  • Data representation and processing

Notes:

• Digital Circuits: Number systems are used in designing logic gates, flip-flops, and other digital components.
• Computer Programming: Hexadecimal and binary are often used in low-level programming, debugging, and memory addressing.
• Data Representation: Data in computers is stored and processed in binary format. Understanding number systems helps in areas like file formats, encryption, and data compression.

Slide 10: Summary and Q&A

• Key Points:
  • Recap of key points
  • Open floor for questions

Notes:

• Summary: Reiterate the importance of understanding different number systems in digital electronics and their practical applications.
• Q&A: Encourage questions to ensure understanding and clarify any doubts.

Additional Content: Visual Aids and Examples

• Visuals:
  • Diagrams of number system conversions
  • Tables showing binary, octal, decimal, and hexadecimal equivalents
  • Flowcharts for conversion processes
• Examples:
  • Sample problems with step-by-step solutions for conversions and arithmetic operations
  • Real-world scenarios like how computers use these number systems for processing and memory storage.                                   created by : Bsant kumar yadav