In binary representation for networking and computing, what is the 8-bit binary form of the decimal number 192?

Introduction:
Fluency converting between decimal and binary is critical for IP addressing, subnet masks, and low-level computing tasks. Recognizing common octet values (such as 192, 224, 240, 248, 252, 254) speeds up subnetting and troubleshooting.

Given Data / Assumptions:

• The value to convert is decimal 192.
• We require an 8-bit (one-octet) binary representation.
• No signed representation complications; this is an unsigned conversion.

Concept / Approach:
Use positional weights of an 8-bit octet: 128, 64, 32, 16, 8, 4, 2, 1. Determine which weights sum to 192. Since 192 = 128 + 64, set the first two bits to 1 and the rest to 0, yielding 11000000.

Step-by-Step Solution:
1) Start with the highest weight ≤ 192 → 128; remainder = 64.2) Next weight 64 fits → set to 1; remainder = 0.3) All lower weights (32..1) must be 0 because remainder is 0.4) Final 8-bit string = 11000000.

Verification / Alternative check:
Compute in reverse: 1*128 + 1*64 + six zeros = 192. Also, note subnet mask patterns: /26 mask value 192 corresponds to 11000000 in the last octet—an easy mnemonic.

Why Other Options Are Wrong:

• 00111110: equals 62 decimal.
• 00001111: equals 15 decimal.
• 00000011: equals 3 decimal.
• None of the above: invalid because 11000000 is correct.

Common Pitfalls:
Confusing /26 mask (192) with /30 (252) or misreading bit order from left to right.

Final Answer:
11000000