Worksheet

A7.6 Error checking and correction

Data representation · A level · AQA 7517 4.5.5.3, Eduqas A500QS 2.8 · about 30 min

What this lesson is about

Parity bits, majority voting, checksums and check digits, with checksums on the robot's radio messages.

• Parity bits
• Majority voting
• Checksums
• Check digits
• Comparing the methods

Questions 6 marks in all

1. [1 mark]Even parity is used. What parity bit is added to the 7 bits 1101011?

2. [1 mark]Even parity is used. The byte 01101011 is received. What can the receiver conclude?

   1. AThere is an error, because the byte has an odd number of 1s
   2. BThe byte is correct
   3. CBit 3 is wrong and can be corrected
   4. DExactly two bits are wrong

3. [1 mark]Majority voting sends each bit three times. The groups 110 011 000 are received. Give the three data bits.

4. [1 mark]Which of these methods can correct an error without the data being sent again?

   Tick every answer that is true.

   1. AMajority voting
   2. BA parity bit
   3. CA checksum
   4. DA check digit

5. [1 mark]A checksum adds the character codes of a message modulo 256. Which error does it always miss?

   1. ATwo characters swapping places
   2. BOne character changed
   3. COne bit flipped
   4. DA character missing

6. [1 mark]What does this program print?

   digits = [9, 7, 8, 1, 8, 6, 1, 9, 7, 8, 2, 7]
   total = 0
   for i in range(12):
       weight = 1 if i % 2 == 0 else 3
       total = total + digits[i] * weight
   print(total, (10 - total % 10) % 10)

The task: checksums on the radio

Write checksum(text). The parameter text is a string. It returns the sum of the character codes (use ord) modulo 256, as a string of exactly two uppercase hex digits (you may use format(n, "02X")). 1. For each command in GO 20, LEFT 90, STOP, in that order, build the packet <command>*<checksum>, send it with send(), and print sent <packet>. Send the packet you built, not typed-in text. 2. For each packet in received, split it at the *, recalculate the checksum of the text part and print <packet> ok if it matches the checksum that arrived, or <packet> corrupt if it does not.

# the two lines every program starts with: the commands, then the robot
from bugbot import *
connect()

def checksum(text):
    return "00"

received = ["GO 20*18", "G0 20*18", "STOP*46", "LEFT 80*B4"]

Plan your program here, then type it in and press Run.

Do it on the robot
www.bugbotlab.com/learn/a7-6-error-checking-and-correction/
The simulator checks it and tells you when it passes. Nothing to install, no account.

Challenges

1. Show a corruption of STOP that the checksum misses.
2. Send each byte of GO three times as bits and write the majority-voting decoder.
3. Weight each character code by its position before adding. Does OG 20 now get a different checksum from GO 20?