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

Day 12 – Chapter 2: Number System Arithmetic

Class 11 Computer Science

2.18 Introduction to Binary Arithmetic (बाइनरी अंकगणित का परिचय)

Binary arithmetic involves operations performed on binary numbers. These operations include addition, subtraction, multiplication, and division, which are essential in computer systems.
बाइनरी अंकगणित में बाइनरी संख्याओं पर किए गए संचालन शामिल हैं। इनमें जोड़, घटाव, गुणा, और भाग शामिल हैं, जो कंप्यूटर प्रणालियों में महत्वपूर्ण हैं।

2.19 Binary Addition (बाइनरी जोड़)

Binary addition is similar to decimal addition. The rules for binary addition are:
बाइनरी जोड़ दशमलव जोड़ के समान है। बाइनरी जोड़ के नियम निम्नलिखित हैं:

• 0 + 0 = 0
• 0 + 1 = 1
• 1 + 0 = 1
• 1 + 1 = 10 (carry 1)

• Example: 1011₂ + 110₂ = 10001₂

2.20 Binary Subtraction (बाइनरी घटाव)

Binary subtraction uses the concept of borrowing, similar to decimal subtraction. The rules for binary subtraction are:
बाइनरी घटाव दशमलव घटाव के समान उधार लेने की अवधारणा का उपयोग करता है। बाइनरी घटाव के नियम निम्नलिखित हैं:

• 0 - 0 = 0
• 1 - 0 = 1
• 1 - 1 = 0
• 0 - 1 = 1 (borrow 1)

• Example: 1011₂ - 110₂ = 101₂

2.21 Binary Multiplication (बाइनरी गुणा)

Binary multiplication is performed similarly to decimal multiplication using repeated addition. The rules for binary multiplication are:
बाइनरी गुणा पुनरावृत्त जोड़ का उपयोग करते हुए दशमलव गुणा के समान किया जाता है। बाइनरी गुणा के नियम निम्नलिखित हैं:

• 0 × 0 = 0
• 0 × 1 = 0
• 1 × 0 = 0
• 1 × 1 = 1

• Example: 101₂ × 11₂ = 1111₂

2.22 Binary Division (बाइनरी भाग)

Binary division is similar to long division in the decimal system. It involves repeated subtraction and shifting.
बाइनरी भाग दशमलव प्रणाली में लंबा भाग के समान है। इसमें पुनरावृत्त घटाव और शिफ्टिंग शामिल है।

• Example: 11010₂ ÷ 10₂ = 1101₂

Practice Questions (अभ्यास प्रश्न)

Multiple Choice Questions (MCQs)

1. What is the sum of 101₂ + 11₂?
   (a) 110₂ | (b) 1000₂ | (c) 1010₂ | (d) 100₂
2. What is 1011₂ - 10₂?
   (a) 1001₂ | (b) 101₂ | (c) 1000₂ | (d) 110₂
3. What is the product of 101₂ × 11₂?
   (a) 111₂ | (b) 1111₂ | (c) 1010₂ | (d) 1101₂
4. What is the quotient of 110₂ ÷ 10₂?
   (a) 11₂ | (b) 10₂ | (c) 1₂ | (d) 100₂
5. What is the result of 1010₂ + 110₂?
   (a) 10000₂ | (b) 1110₂ | (c) 1011₂ | (d) 1100₂
6. What is the binary representation of 27₁₀?
   (a) 11011₂ | (b) 10111₂ | (c) 11101₂ | (d) 10011₂
7. What is the binary equivalent of 15₁₀?
   (a) 1001₂ | (b) 1101₂ | (c) 1111₂ | (d) 1011₂
8. What is 1011₂ ÷ 11₂?
   (a) 11₂ | (b) 10₂ | (c) 1₂ | (d) 101₂
9. Which operation is performed by repeated subtraction in binary?
   (a) Addition | (b) Subtraction | (c) Division | (d) Multiplication
10. What is the binary product of 11₂ × 10₂?
    (a) 110₂ | (b) 1000₂ | (c) 1010₂ | (d) 111₂

Answers to MCQs:

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

Short Answer Questions (लघु उत्तरीय प्रश्न)

1. What are the rules for binary addition?
   Answer: 0+0=0, 0+1=1, 1+0=1, 1+1=10 (carry 1).
2. What is 1011₂ - 11₂?
   Answer: 1000₂.
3. Explain binary multiplication rules.
   Answer: 0×0=0, 0×1=0, 1×0=0, 1×1=1.
4. How is binary division performed?
   Answer: By repeated subtraction and shifting.
5. What is the binary equivalent of 19₁₀?
   Answer: 10011₂.

Long Answer Questions (दीर्घ उत्तरीय प्रश्न)

1. Explain the process of binary addition and subtraction with examples.
2. Discuss binary multiplication and its importance in computer arithmetic.
3. Describe the steps involved in binary division with an example.