BCD conversion and addition — add 275 and 965 in BCD Convert the decimal numbers 275 and 965 to BCD, perform BCD addition, and select the BCD groups that represent the final sum (thousands to ones).

Introduction / Context:Binary-coded decimal (BCD) represents each decimal digit with its own 4-bit code, which is common in digital displays and decimal arithmetic units. This task checks your ability to encode, add, and recognize the BCD result.

Given Data / Assumptions:

• Numbers: 275 and 965 (decimal).
• BCD digit mapping: 0→0000, 1→0001, …, 9→1001.
• Use BCD addition with decimal correction when a digit sum exceeds 9.

Concept / Approach:

Add the decimal numbers first to know the expected result, then encode that result into BCD. Alternatively, convert each operand to BCD, add digit-wise, and apply a +6 correction (0110) to any digit sum greater than 9 to restore valid BCD and propagate carries.

Step-by-Step Solution:

Verification / Alternative check:

Digit-wise BCD add: 5 + 5 = 10 → write 0, carry 1; 7 + 6 + 1 = 14 → write 4, carry 1; 2 + 9 + 1 = 12 → write 2, carry 1 to thousands → 1. Encoded result is identical to the direct conversion of 1240.

Why Other Options Are Wrong:

• Options a, b: not valid BCD for 1240; include invalid digit codes or wrong order.
• Option d: 2 3 4 0 (2340), not 1240.
• Option e: 1 2 3 8 (1238), not 1240.

Common Pitfalls:

• Treating 1240 as a binary number rather than BCD groups.
• Forgetting the +6 correction in BCD digit sums above 9.

Final Answer:

0001 0010 0100 0000