Basic Flashcards

General topic for this subcategory

What are the 4 main number systems in computing?

Binary (base-2, digits 0-1), Octal (base-8, digits 0-7), Decimal (base-10, digits 0-9), Hexadecimal (base-16, digits 0-9, A-F).

Convert 1010₂ to Decimal

1×2³ + 0×2² + 1×2¹ + 0×2⁰ = 8 + 0 + 2 + 0 = 10₁₀

Convert 25₁₀ to Binary

Divide by 2 repeatedly: 25÷2=12r1 → 12÷2=6r0 → 6÷2=3r0 → 3÷2=1r1 → 1÷2=0r1. Read remainders upward: 11001₂

Convert FF₁₆ to Decimal

F = 15. FF₁₆ = 15×16¹ + 15×16⁰ = 240 + 15 = 255₁₀

Convert 255₁₀ to Hexadecimal

255÷16=15 remainder 15. 15=F, 15=F → FF₁₆

Convert 1111₂ to Hexadecimal

Group binary digits in 4s: 1111₂ = F₁₆ (since F=15 in decimal).

Convert 10101100₂ to Hexadecimal

Split into groups of 4: 1010=A, 1100=C → AC₁₆

Convert 777₈ (Octal) to Decimal

7×8² + 7×8¹ + 7×8⁰ = 448 + 56 + 7 = 511₁₀

What is 1's complement?

1's complement of a binary number is obtained by flipping all bits: 0→1 and 1→0. Example: 1010 → 0101.

What is 2's complement?

2's complement = 1's complement + 1. Used to represent negative numbers in binary. Example: -5 in 8-bit = 11111011.

What is the decimal (base-10) system?

The decimal system uses 10 digits (0–9). Each digit position represents a power of 10. It is the standard system for everyday use.

Convert 0.5₁₀ to Binary

Multiply by 2 repeatedly: 0.5×2=1.0 → stop. Answer: 0.1₂

What is a prime number?

A prime number is a natural number greater than 1 with exactly two factors: 1 and itself. Examples: 2, 3, 5, 7, 11, 13.

What are divisibility rules?

Div by 2: even last digit. Div by 3: digit sum divisible by 3. Div by 5: ends in 0 or 5. Div by 9: digit sum divisible by 9.

What is HCF (GCD)?

HCF (Highest Common Factor) is the largest number that divides two or more numbers exactly. Found by prime factorisation or Euclidean algorithm.

What is LCM?

LCM (Least Common Multiple) is the smallest number divisible by two or more given numbers. LCM × HCF = product of two numbers.