Number systems conversion (decimal to binary with fractional part): Convert the decimal number 6.75 to binary, using a fixed-point representation with four fractional bits.

Introduction / Context:
Converting decimal numbers with fractional parts to binary is fundamental in digital systems, especially for fixed-point representation and understanding DAC/ADC step sizes and quantization.

Given Data / Assumptions:

• Decimal value: 6.75.
• Binary output should show an integer part and four fractional bits.
• Unsigned positive representation is assumed.

Concept / Approach:
Split into integer and fractional parts. Convert the integer by successive division by 2. Convert the fraction by successive multiplication by 2, recording carries.

Step-by-Step Solution:
Integer 6 → binary: 6 / 2 = 3 r0; 3 / 2 = 1 r1; 1 / 2 = 0 r1 → read MSB to LSB: 110.Fraction .75 → multiply by 2: 0.752 = 1.5 → bit 1, remainder .5..52 = 1.0 → bit 1, remainder .0.With four fractional bits, pad trailing zeros → .1100.Combine: 110.1100. With leading zero formatting to 4 bits integer: 0110.1100.

Verification / Alternative check:
Back to decimal: 0110.1100 = 6 + 0.5 + 0.25 = 6.75. Correct.

Why Other Options Are Wrong:
0111.1100 = 7.75.0110.1010 = 6.625.0110.0110 = 6.375.110.11 is numerically correct (6.75) but does not match the requested four fractional-bit fixed-point formatting used in the options.

Common Pitfalls:
Stopping fractional conversion too soon or forgetting to pad to a defined number of fractional bits can cause mismatch with fixed-point option formats.

Final Answer:
0110.1100