Binary conversion practice: convert the decimal number 224 to its 8-bit binary representation.

Introduction / Context:
Converting between decimal and binary is a foundational skill in computer science and networking. IP addressing, subnet masks, and many low-level operations rely on bitwise reasoning. Here we convert the decimal value 224 into an 8-bit binary string suitable for byte-oriented contexts (e.g., subnet masks such as 255.255.255.224).

Given Data / Assumptions:

• We need an 8-bit representation (values 0–255).
• Decimal input is 224.
• Standard positional weights are 128, 64, 32, 16, 8, 4, 2, 1.

Concept / Approach:
Binary expansion expresses a number as a sum of powers of 2. Determine which place values are needed by subtracting the largest possible powers of 2 without making the running total negative. Place a 1 where a weight is used and a 0 where it is not.

Step-by-Step Solution:

Verification / Alternative check:
Reconstruct from bits: 1128 + 164 + 132 + 016 + 08 + 04 + 02 + 01 = 224, confirming correctness.

Why Other Options Are Wrong:

Common Pitfalls:
Reversing bit order (LSB/MSB confusion) or stopping after setting the first few bits without confirming the remainder is zero.

Final Answer:
11100000.