Decimal to 8-bit binary — encode the value with leading zeros if needed. Task: Convert 187₁₀ to an 8-bit binary representation.

Introduction / Context:
Encoding a decimal integer as an 8-bit binary pattern is common when writing to registers, configuring peripherals, or defining bit masks. The 8-bit form explicitly shows each bit from 2^7 to 2^0.

Given Data / Assumptions:

• Decimal value: 187
• Target width: 8 bits (MSB first)

Concept / Approach:
Decompose 187 into powers of two ≤ 128. Mark a 1 for each included power and 0 otherwise to build the 8-bit string. Alternatively, perform repeated division by 2 and pad to 8 bits.

Step-by-Step Solution:

Verification / Alternative check:
Sum the active weights: 128 + 32 + 16 + 8 + 2 + 1 = 187. Also, a calculator check in binary mode will show 187 → 10111011₂.

Why Other Options Are Wrong:

• 11011101, 10111101, 10111100, 10111010: each flips or misses one or more required bit positions.

Common Pitfalls:

• Forgetting the 64’s place is 0 here, or misplacing the 4’s place (which is 0).

Final Answer:
10111011