Check a Simple Parity Rule

Supplied materials

• Paper and pencil. Supplied toy rule: append one check bit so the total number of 1s is even. No network or software is required.

Learn the idea

An error-detection rule can flag some changes without telling us exactly which bit changed. Here the data is four bits and the fifth bit is an even-parity check bit. Choose that last bit so the total number of 1s in all five bits is even. This is a toy check, not encryption or a complete reliability guarantee.

Data 1011 contains three 1s, an odd count, so append 1 to produce 10111 with four 1s. A receiver counts the 1s in the five-bit message. An odd count flags a parity error. A single flipped bit changes the parity, but flipping two bits can leave it even and escape this check.

1. Count the 1s in four-bit data 1011.
2. Append the check bit needed for an even total.
3. Flip the first bit to get 00111 and recount.
4. Flip both the first and second bits of the original message to get 01111 and compare the check result.

Check your reasoning

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Take it further

Change data to 0001. Expected appended bit: 1, producing 00011 with two 1s. Flip its last data bit to 0: message 00001 has one 1 and fails the check.

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