Hexadecimal conversion: what is the hexadecimal equivalent of the binary number 10101111 (base 2)?

Introduction / Context:Binary-to-hex conversion is convenient because each hex digit corresponds to 4 binary bits. This mapping avoids lengthy decimal conversions and is widely used in debugging, memory dumps, and instruction encoding.

Given Data / Assumptions:

• Binary value: 10101111₂.
• We will group the bits in nibbles (4-bit groups).
• No sign or fractional parts are involved.

Concept / Approach:Split into nibbles: 1010 1111. Translate: 1010₂ = A₁₆ and 1111₂ = F₁₆. Thus, the hexadecimal representation is AF₁₆.

Step-by-Step Solution:

Verification / Alternative check:Decimal check: 10101111₂ = 175₁₀; AF₁₆ = 10*16 + 15 = 175, confirming equivalence.

Why Other Options Are Wrong:

Common Pitfalls:Misgrouping bits from the left; forgetting that 1111 equals F, not E.

Final Answer:AF