Binary to hexadecimal conversion: What is the hexadecimal equivalent of the binary number 110000₂?

Introduction / Context:Hexadecimal (base 16) is convenient for expressing binary values compactly because 16 = 2^4, so each hex digit maps to exactly four binary bits. Converting binary to hex is a matter of grouping bits into 4-bit chunks and translating each group.

Given Data / Assumptions:

• Binary input: 110000₂.
• Target representation: hexadecimal (base 16).
• No change in numeric value—only the base changes.

Concept / Approach:Group the binary number into 4-bit nibbles from the right. If the most significant group has fewer than 4 bits, pad with leading zeros. Then use the binary-to-hex table: 0000→0, 0001→1, …, 1111→F.

Step-by-Step Solution:Write 110000₂ as 0011 0000₂ to form two 4-bit groups.Translate 0011₂ → 3₁₆.Translate 0000₂ → 0₁₆.Combine: 0x30 → written as 3016.

Verification / Alternative check:Decimal cross-check: 110000₂ = 48₁₀; 48 / 16 = 3 remainder 0, so 0x30 (3016). Both methods agree.

Why Other Options Are Wrong:4016, 4316, and 2716 correspond to different binary values. Only 3016 matches 110000₂ exactly.

Common Pitfalls:Forgetting to pad the most significant bits to multiples of four; misreading 0011 as 4 instead of 3.

Final Answer:3016