BCD versus pure binary – convert the BCD number 1000 0001 (representing the decimal value 81) into its equivalent straight binary, expressed as an 8-bit group.

Introduction / Context: Binary Coded Decimal (BCD) encodes each decimal digit separately using four bits. Converting a BCD representation to straight binary requires interpreting the two nibbles as decimal digits and then converting the resulting decimal value into ordinary base-2 form. Here, the BCD bits 1000 0001 indicate the decimal number 81; we must produce its binary equivalent as an 8-bit group for clarity and alignment with common register widths.

Given Data / Assumptions:

• BCD 1000 0001 → high nibble 1000 (8), low nibble 0001 (1).
• Decimal value = 81.
• Output format requested: straight binary, 8 bits grouped as xxxx xxxx.

Concept / Approach: First read the BCD nibbles to determine the decimal value. Then convert that decimal number to ordinary binary. For 81, compute the powers of two that sum to 81: 64 + 16 + 1. This directly yields the 8-bit pattern by setting bits corresponding to 64, 16, and 1, with all others cleared. Formatting with a space after four bits aids readability without changing the value.

Step-by-Step Solution:

Verification / Alternative check: Long division by 2: 81/2 → remainders 1010001; pad to 8 bits → 0101 0001, matching the computed sum-of-powers form.

Why Other Options Are Wrong: 0110 0011 = 99; 0100 0001 = 65; 1000 0000 = 128; 0011 0010 = 50. None equal 81.

Common Pitfalls: Treating the BCD nibbles as a single 8-bit binary value (which would be 129), forgetting that BCD must be converted via its decimal meaning; dropping leading zeros in 8-bit formatting.

Final Answer: 0101 0001