Convert the decimal value 240 into its 8-bit binary representation. Choose the correct binary pattern.

Introduction / Context: Number base conversions are foundational in computer science. Binary representations map directly to bit fields, masks, and hardware registers. Converting a decimal number to 8-bit binary requires decomposing it into powers of two and ensuring the result fits within the standard byte width.

Given Data / Assumptions:

• Decimal number: 240.
• We need an 8-bit (one byte) binary representation.
• No two’s-complement sign handling is required since 240 is nonnegative.

Concept / Approach: Express the number as a sum of powers of two: 128, 64, 32, 16, 8, 4, 2, 1. Starting from the largest power less than or equal to the number, mark a 1 when included and subtract it; otherwise, mark a 0 and continue. The remaining least significant bits follow the same pattern until the sum equals the target number.

Step-by-Step Solution: Largest power of two ≤ 240 is 128 → set bit7 = 1; remainder 112.Next 64 → set bit6 = 1; remainder 48.Next 32 → set bit5 = 1; remainder 16.Next 16 → set bit4 = 1; remainder 0.Remaining bits (8, 4, 2, 1) are not needed → set bits3..0 = 0.Thus the 8-bit pattern is 11110000.

Verification / Alternative check: Add back the set weights: 128 + 64 + 32 + 16 = 240, confirming the binary string 11110000. As a hexadecimal cross-check, 240 = 0xF0, which corresponds to binary 1111 0000.

Why Other Options Are Wrong: 00011110: Equals 30 decimal, not 240.

00001111: Equals 15 decimal.

11100000: Equals 224 decimal.

None of the above: Incorrect because 11110000 is correct.

Common Pitfalls: Forgetting to use exactly 8 bits (leading zeros omitted) or mis-summing powers of two. Writing 0xF0 directly helps avoid mistakes: F = 1111, 0 = 0000.

Final Answer: 11110000