Day 7: Binary Arithmetic – Addition, Subtraction, Multiplication, and Division | Class 11 - BSEB Class 11-12 Computer Science: 100-Day Bilingual Guide with MCQs, Solutions and Questions

Day 7 – Chapter 2: Binary Arithmetic

Class 11 Computer Science

2.4 Introduction to Binary Arithmetic (बाइनरी अंकगणित का परिचय)

Binary arithmetic is a fundamental operation in computer systems, performed using binary numbers. Computers rely on binary operations for data processing.
बाइनरी अंकगणित कंप्यूटर प्रणालियों में मौलिक संचालन है, जो बाइनरी संख्याओं का उपयोग करके किया जाता है। कंप्यूटर डेटा प्रोसेसिंग के लिए बाइनरी संचालन पर निर्भर करते हैं।

2.5 Operations in Binary Arithmetic (बाइनरी अंकगणित में संचालन)

2.5.1 Binary Addition (बाइनरी जोड़)

Binary addition is performed like decimal addition, with a carryover when the sum exceeds 1.
बाइनरी जोड़ दशमलव जोड़ की तरह किया जाता है, जिसमें योग 1 से अधिक होने पर कैरीओवर होता है।

• Rules:
  • 0 + 0 = 0
  • 0 + 1 = 1
  • 1 + 0 = 1
  • 1 + 1 = 10 (carry 1)
• Example: 101₂ + 110₂ = 1011₂

2.5.2 Binary Subtraction (बाइनरी घटाव)

Binary subtraction involves borrowing, similar to decimal subtraction.
बाइनरी घटाव उधार लेने पर आधारित होता है, जो दशमलव घटाव के समान है।

• Rules:
  • 0 - 0 = 0
  • 1 - 0 = 1
  • 1 - 1 = 0
  • 0 - 1 = 1 (borrow 1)
• Example: 1101₂ - 101₂ = 1000₂

2.5.3 Binary Multiplication (बाइनरी गुणा)

Binary multiplication is performed using repeated addition or the AND operation.
बाइनरी गुणा पुनरावृत्त जोड़ या AND ऑपरेशन का उपयोग करके किया जाता है।

• Rules:
  • 0 × 0 = 0
  • 0 × 1 = 0
  • 1 × 0 = 0
  • 1 × 1 = 1
• Example: 101₂ × 11₂ = 1111₂

2.5.4 Binary Division (बाइनरी भाग)

Binary division follows the rules of long division in the decimal system.
बाइनरी भाग दशमलव प्रणाली में दीर्घ भाग के नियमों का पालन करता है।

• Example: 110₂ ÷ 10₂ = 11₂ (Quotient) and 0₂ (Remainder)

Practice Questions (अभ्यास प्रश्न)

Multiple Choice Questions (MCQs)

1. What is the sum of 101₂ + 11₂?
   (a) 111₂ | (b) 1000₂ | (c) 110₂ | (d) 1011₂
2. What is 1101₂ - 101₂?
   (a) 100₂ | (b) 1010₂ | (c) 1000₂ | (d) 111₂
3. What is the binary product of 101₂ × 10₂?
   (a) 101₂ | (b) 1010₂ | (c) 111₂ | (d) 1001₂
4. What is the quotient of 111₂ ÷ 11₂?
   (a) 1₂ | (b) 11₂ | (c) 101₂ | (d) 10₂
5. What is 1010₂ + 110₂?
   (a) 10000₂ | (b) 1110₂ | (c) 1001₂ | (d) 1011₂
6. What is 1011₂ - 101₂?
   (a) 1001₂ | (b) 101₂ | (c) 111₂ | (d) 110₂
7. What is the binary equivalent of 7?
   (a) 111₂ | (b) 101₂ | (c) 11₂ | (d) 100₂
8. What is the product of 11₂ × 11₂?
   (a) 101₂ | (b) 111₂ | (c) 1001₂ | (d) 110₂
9. What is the binary addition result of 111₂ + 111₂?
   (a) 1010₂ | (b) 1110₂ | (c) 1101₂ | (d) 1011₂
10. Which operation involves borrowing in binary arithmetic?
    (a) Addition | (b) Subtraction | (c) Multiplication | (d) Division

Answers to MCQs:

1: (a), 2: (c), 3: (b), 4: (d), 5: (b), 6: (c), 7: (a), 8: (c), 9: (b), 10: (b)

Short Answer Questions (लघु उत्तरीय प्रश्न)

1. Define binary addition. Provide an example.
   Answer: Binary addition is the process of adding binary numbers. Example: 101₂ + 11₂ = 1000₂.
2. Explain binary subtraction with an example.
   Answer: Binary subtraction is the process of subtracting binary numbers. Example: 1101₂ - 101₂ = 1000₂.
3. What is the product of 101₂ × 11₂?
   Answer: 1111₂.
4. How does binary division differ from decimal division?
   Answer: Binary division operates on binary numbers using repeated subtraction and shifting, unlike decimal division which uses base 10.
5. Why is binary arithmetic critical in computing?
   Answer: Binary arithmetic is essential because computers process all data in binary format for calculations, logic, and data manipulation.

Long Answer Questions (दीर्घ उत्तरीय प्रश्न)

1. Explain the rules of binary addition and subtraction with detailed examples.
2. Discuss the importance of binary multiplication and division in computer operations. Provide examples.
3. How does binary arithmetic form the foundation of all computer operations? Discuss its significance in programming and data processing.