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1) Binary to Decimal Conversion

To convert a binary number to decimal, multiply each bit by its place value (2⁰, 2¹, 2², etc.) then add the results.
Example: 1011₂ = (1×2³) + (0×2²) + (1×2¹) + (1×2⁰) = 8 + 0 + 2 + 1 = 11 (decimal).


2) Advantages of Universal Gates

Universal gates are NAND and NOR gates. Their advantage is that any logical function can be implemented using just one type of gate. This makes design simpler, reduces manufacturing cost, and increases flexibility in

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Logical organisation of computer number system

(a) What is a Number System?

A number system is a way of representing numbers using a set of symbols and a base (radix).
Examples:

Decimal (base 10)

Binary (base 2)

Octal (base 8)

Hexadecimal (base 16

b) Why Digital Computers use Binary Number System?

Digital computers use binary because:

Electronic circuits have two states: ON (1) and OFF (0)

Binary is reliable and easy to implement

Less error in data processing

(c) Convert (1001.0010)₂ to Decimal

Integer part:
10012=1×23+0×22+0×21+1×20=91001₂

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QUESTION 1 (Compulsory – Short Answers)

(a) What is a Number System?

A number system is a way of representing numbers using a set of symbols and a base (radix).
Examples:

  • Decimal (base 10)

  • Binary (base 2)

  • Octal (base 8)

  • Hexadecimal (base 16)


(b) Why Digital Computers use Binary Number System?

Digital computers use binary because:

  • Electronic circuits have two states: ON (1) and OFF (0)

  • Binary is reliable and easy to implement

  • Less error in data processing


(c) Convert (1001.

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As physical and hormonal changes peak, adolescents face critical health choices regarding nutrition and substance use. These issues are deeply interconnected with the brain development we discussed earlier—the struggle between a seeking "reward system" and a still-developing "control center."
1. Nutrition and Growth -The "growth spurt" in adolescence creates the highest nutritional demand of any life stage except infancy. * Nutrient Demands: The body requires massive increases in calcium (for bone

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प्रश्न 2 (a) : इंजन के भागों के कार्य (स्केच सहित)

(i) Cylinder Head

  • सिलेंडर के ऊपरी भाग को बंद करता है

  • इसमें वाल्व, स्पार्क प्लग / इंजेक्टर लगे होते हैं

  • दहन कक्ष का निर्माण करता है

(ii) Piston Rings

  • गैस लीकेज रोकती हैं

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ਬਬਬਜਰਜਰਜਫਜ਼ਜ਼ੀਰ

ਪੰਜਾਬੀ ਵਿੱਚ ਸ਼ਬਦ ਰਚਨਾ (Word Formation) ਦੇ ਦੋ ਪ੍ਰਮੁੱਖ ਤਰੀਕੇ ਹਨ: ਅਗੇਤਰ ਅਤੇ ਪਿਛੇਤਰ। ਇਹਨਾਂ ਦੀ ਵਰਤੋਂ ਮੂਲ ਸ਼ਬਦਾਂ ਤੋਂ ਨਵੇਂ ਸ਼ਬਦ ਬਣਾਉਣ ਲਈ ਕੀਤੀ ਜਾਂਦੀ ਹੈ।
1. ਅਗੇਤਰ (Prefixes) -ਜਿਹੜੇ ਸ਼ਬਦ-ਅੰਸ਼ ਮੂਲ ਸ਼ਬਦ ਦੇ ਸ਼ੁਰੂ ਵਿੱਚ ਲੱਗ ਕੇ ਉਸ

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ਧੁਨੀ ਬੋਧ (Phonology) ਅਤੇ ਅੱਖਰ ਬੋਧ (Orthography) ਪੰਜਾਬੀ ਵਿਆਕਰਨ ਦਾ ਪਹਿਲਾ ਅਤੇ ਮਹੱਤਵਪੂਰਨ ਭਾਗ ਹਨ। ਇਸ ਵਿੱਚ ਭਾਸ਼ਾ ਦੀਆਂ ਸਭ ਤੋਂ ਛੋਟੀਆਂ ਇਕਾਈਆਂ—ਧੁਨੀਆਂ ਅਤੇ ਉਹਨਾਂ ਨੂੰ ਲਿਖਣ ਲਈ ਵਰਤੇ ਜਾਂਦੇ ਚਿੰਨ੍ਹਾਂ (ਅੱਖਰਾਂ) ਬਾਰੇ ਜਾਣਕਾਰੀ ਮਿਲਦੀ

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Supply chain

1. What are the factors influencing network design? (VTU – 10 Marks Answer)
Introduction: Supply chain network design involves decisions related to facility location, capacity, and market allocation. These decisions are strategic and long-term in nature and directly influence cost, responsiveness, and overall supply chain performance.
Factors Influencing Network Design: Strategic Factors: A firm’s competitive strategy strongly impacts network design. Cost leadership firms prefer low-cost locations,

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1) Recurrences

1.1 10-mark: Solve T(n)=2T(n/2)+n, T(1)=c

T(n)=2T(n/2)+n
=4T(n/4)+2n
=8T(n/8)+3n
... after i steps: T(n)=2^i T(n/2^i) + i*n
Stop: n/2^i=1 => i=log2 n
T(n)=n*T(1) + n log2 n = n*c + n log2 n
=> T(n)=Theta(n log n)

1.2 Master theorem (write as-is)

T(n)=aT(n/b)+f(n), compare f(n) with n^{log_b a}
Case1: f(n)=O(n^{log_b a - eps}) => T(n)=Theta(n^{log_b a})
Case2: f(n)=Theta(n^{log_b a} log^k n) => T(n)=Theta(n^{log_b a} log^{k+1} n)
Case3: f(n)=Omega(n^{log_b a + eps}) and a f(n/b)

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