Even parity encoding for a given value: Represent decimal 37 using binary along with an even parity bit (assume the parity bit is placed as the most significant bit of an 8-bit pattern). Which option matches?

Introduction / Context:
Parity bits add minimal redundancy to detect transmission errors. In many examples, a single parity bit is prepended as the most significant bit, forming an 8-bit pattern from a 7-bit data value. This question asks which 8-bit pattern correctly represents decimal 37 with even parity when the parity bit is the MSB.

Given Data / Assumptions:

• Decimal 37 in binary (7-bit data) is 0100101.
• Parity scheme: even parity, parity bit placed as MSB.
• Total number of 1s across all 8 bits must be even.

Concept / Approach:
Compute the binary of the data value, count the number of 1s, and choose the parity bit so that the total count is even. Then confirm the option whose MSB matches the required parity while the lower 7 bits match the data.

Step-by-Step Solution:

Verification / Alternative check:
Count ones in 10100101: there are 4 ones — even. The lower 7 bits still equal 0100101, confirming the data value is intact and parity is correct.

Why Other Options Are Wrong:

Common Pitfalls:
Forgetting whether the parity bit is MSB or LSB in a given protocol; miscounting ones; writing 8-bit binary for 37 (00100101) and treating its MSB as parity when it is actually a data bit in that representation.

Final Answer:
10100101