Decimal to binary conversion The decimal number 188 is equal to which binary (base 2) representation?

Introduction / Context:
Converting decimal to binary is fundamental for digital design. The standard technique uses successive division by 2 or decomposition into powers of two that sum to the target value.

Given Data / Assumptions:

• Target decimal value: 188.
• Powers of two near 188: 128, 64, 32, 16, 8, 4, 2, 1.

Concept / Approach:
Express 188 as a sum of powers of two, then place 1s in those bit positions and 0s elsewhere. Alternatively, use repeated division by 2 and collect remainders from last to first.

Step-by-Step Solution:

Verification / Alternative check:
Compute back: 128 + 32 + 16 + 8 + 4 = 188, matching the pattern 10111100₂.

Why Other Options Are Wrong:

• 0111000 / 1100011 / 1111000: Different bit sums that evaluate to other decimal values, not 188.

Common Pitfalls:
Missing a needed power (for example, forgetting 4) or misplacing zeros when writing the final 8-bit form.

Final Answer:
10111100