Number systems — convert the binary value to hexadecimal. Task: Convert binary 1001₂ into its equivalent hexadecimal form and choose the correct option.

Introduction / Context:Binary-to-hexadecimal conversion is fundamental in digital electronics and computer architecture. Because 1 hexadecimal digit corresponds exactly to 4 binary bits, grouping bits into nibbles (4-bit groups) makes conversion fast and error-resistant.

Given Data / Assumptions:

• Binary number: 1001
• We need the hexadecimal (base 16) equivalent
• No sign or fractional part is involved

Concept / Approach:Map each 4-bit binary nibble to one hexadecimal digit using the standard 0–15 (0–F) correspondence. The nibble 1001₂ equals 9 in decimal, which is 9 in hexadecimal as well. Thus 1001₂ → 9₁₆.

Step-by-Step Solution:

Verification / Alternative check:You can also convert to decimal first: 1001₂ = 9₁₀, and then to hexadecimal, 9₁₀ = 9₁₆. Both methods agree.

Why Other Options Are Wrong:

• 1116, 10116: imply values 17₁₀ and 257₁₀ respectively, not equal to 9.
• 1016: equals decimal 16 + 0 + 1 = 17 (hex 11), not 9.
• 1216: equals 18₁₀, not 9.

Common Pitfalls:

• Failing to group bits in sets of four or misreading the 8-4-2-1 weights.

Final Answer:916