📚 Knowledge Library — Topic 2.5A — Data Transmission

Error Detection Parity

Understand how parity bits help computers spot transmission errors by counting the number of 1s in binary data.

Start LearningWorked Example
1. Invitation

Data can change on the journey.

When data is transmitted, a bit can sometimes change from 0 to 1, or from 1 to 0.

Error detection checks the received data and spots when something looks wrong.

💡 Remember: error detection finds possible mistakes. It does not automatically fix the original data.
Figure 1.1
Bit Error
Sent: 10110010
↓
Received: 10111010
One bit has changed during transmission.
2. Big Idea

Parity checks count the 1s.

A parity check uses an extra bit called a parity bit.

The parity bit is chosen so the total number of 1s matches the agreed rule: even parity or odd parity.

💡 Parity is a counting check.
Figure 2.1
Counting Ones
1011001
+
parity bit
↓
total 1s checked
3. Bridge

Think of counting coins.

Imagine agreeing that every money bag must contain an even number of gold coins.

Before sending the bag, you add one extra coin if needed. The receiver counts again. If the count is wrong, something has changed.

💡 The parity bit is like the extra coin that makes the count match the rule.
Figure 3.1
Coin Count Model
Gold coins
↓
Count them
↓
Even or odd?
4. Worked Example

Even parity example.

With even parity, the total number of 1s must be even.

Data bits: 1011001

Data
Number of 1s
Parity bit
1011001
4
0
4 is already even, so the parity bit is 0.
Figure 4.1
Even Parity
1011001 + 0
↓
4 ones
↓
even ✓
5. Worked Example

Odd parity example.

With odd parity, the total number of 1s must be odd.

Data bits: 1011001

Data
Number of 1s
Parity bit
1011001
4
1
4 is even, so add 1 to make the total odd.
Figure 5.1
Odd Parity
1011001 + 1
↓
5 ones
↓
odd ✓
6. Exam Tip

The parity bit does not name the parity type.

The parity bit is not a label saying “even” or “odd”.

It is just a 0 or 1 added to make the total number of 1s match the agreed parity rule.

🎯 Exam Tip: count the 1s first. Then decide whether the parity bit should be 0 or 1.
Figure 6.1
Correct Method
Count 1s
↓
Check rule
↓
Add 0 or 1
7. Common Mistake

Parity cannot detect every error.

Parity is useful, but it has limits.

If two bits change, the total number of 1s may still look correct, so the error may not be detected.

⚠️ Common Mistake: saying parity finds all errors. It can miss errors when an even number of bits change.
Figure 7.1
Two Bit Error
10110010
↓ two bits change
10010011

count may still pass
8. Summary

Parity in one screen.

Parity checks detect possible transmission errors by counting the number of 1s.

Even parity means the total number of 1s must be even. Odd parity means the total number of 1s must be odd.

The sender adds a parity bit. The receiver counts again after transmission.

💡 Key idea: parity is a simple error detection method based on counting 1s.
Figure 8.1
Parity Check Flow
Sender counts
↓
Adds parity bit
↓
Receiver counts
↓
Pass or error