A student is learning about the four commonly used number systems in Computer…
2026
A student is learning about the four commonly used number systems in Computer Science: Binary (Base 2), Octal (Base 8), Decimal (Base 10) and Hexadecimal (Base 16). Based on the concepts of number system representation and conversion, help her by answering the following questions.
(A) List all the valid digits that can be used in a Hexadecimal number system.
(B) Convert the Binary number (1110110)₂ into its Decimal equivalent.
(C) Convert the Decimal number (365)₁₀ into its Octal equivalent.
(D) Convert the Octal number (404)₈ into its Binary equivalent.
Show answer & explanation
(A) Hexadecimal digits: 0–9, A–F (A=10, B=11, … F=15).
(B) (1110110)₂ → Decimal
= 1×2⁶ + 1×2⁵ + 1×2⁴ + 0×2³ + 1×2² + 1×2¹ + 0×2⁰
= 64 + 32 + 16 + 0 + 4 + 2 + 0 = 118₁₀
(C) (365)₁₀ → Octal (division by 8):
365 ÷ 8 = 45 r5
45 ÷ 8 = 5 r5
5 ÷ 8 = 0 r5
⇒ (555)₈
(D) (404)₈ → Binary (3-bit method):
4 → 100, 0 → 000, 4 → 100
⇒ 100000100₂
Conclusion: Base conversion uses place value and repeated division methods.