data representation and basic computer arithmetic

Understanding BCA Syllabus Avadh University – Semester I Paper BCA102 T Unit II

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Semester I BCA Syllabus BCA102 T – Computer System Architecture

Semester I Paper BCA101 T Unit II – Data Representation and Basic Computer Arithmetic:

Introduction: Welcome to the fascinating world of Data Representation and Basic Computer Arithmetic. In this Unit, we will dive into the fundamental concepts that form the backbone of computer system architecture. By the end of this Unit, you will have a solid understanding of number systems, data representation, and essential arithmetic operations in computing.

  1. Number Systems
  2. Complements
  3. Fixed and Floating Point Representation
  4. Character Representation
  5. Addition
  6. Substraction
  7. Magnitude Comparison
  8. Multiplication and Division Algorithms for Integers

1. Number Systems: Let’s start our journey with number systems, the foundation of all data representation in computers. We commonly use three number systems:

  • Binary (base 2)
  • Decimal (base 10)
  • Hexadecimal (base 16)

Example:

  • Binary: 1010
  • Decimal: 10
  • Hexadecimal: A

2. Complements: Understanding complements is vital. We have two main types:

  • Two’s Complement (for signed integers)
  • One’s Complement (less common)

Example:

  • Two’s Complement of 5: 1011 (in 4 bits)

3. Fixed and Floating-Point Representation:

  • Fixed-point is suitable for integers and fixed precision.
  • A floating point is used for real numbers with varying precision.

Example:

  • Fixed-point: 7.25 (3 bits for integer, 2 bits for fraction)
  • Floating-point: 1.101 * 2^2

4. Character Representation: Characters are represented using ASCII or Unicode. For instance, ‘A’ is represented as 65 in ASCII.

5. Arithmetic Operations:

a. Addition:

  • Binary addition, just like in decimal.

Example:

  • 1101 (13 in decimal) + 1010 (10 in decimal) = 11011 (19 in decimal)

b. Subtraction:

  • Binary subtraction is similar to decimal subtraction.

Example:

  • 1101 (13 in decimal) – 1010 (10 in decimal) = 11 (3 in decimal)

c. Magnitude Comparison:

  • Comparing two numbers for magnitude.

Example:

  • Is 1010 greater than 1101?

d. Multiplication and Division Algorithms for Integers:

i. Multiplication:

  • Binary multiplication, like long multiplication in decimal.

Example:

  • 1101 (13 in decimal) * 1010 (10 in decimal) = 1111010 (90 in decimal)

ii. Division:

  • Binary division is similar to long division in decimal.

Example:

  • 1101 (13 in decimal) ÷ 1010 (10 in decimal) = 1 with a remainder of 11

Conclusion: We have explored the core concepts of Data Representation and Basic Computer Arithmetic. These fundamentals are crucial in understanding how computers process data. In future modules, we’ll build on this knowledge to explore more advanced topics in computer architecture. Keep practicing and stay curious!

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