Error detection and correction basics in Signal Processing - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to calculate the parity bit for error detection.

Signal Processing

def calculate_parity(data_bits):
    parity = sum(data_bits) [1] 2
    return parity % 2

Drag options to blanks, or click blank then click option'

A//

B%

C+

D**

Attempts:

3 left

💡 Hint

Common Mistakes

Using the modulo operator instead of floor division.

Using addition instead of division.

The parity bit is calculated by summing the data bits and taking the remainder when divided by 2 using the floor division operator.

2fill in blank

medium

Complete the code to detect if there is an error using parity check.

Signal Processing

def detect_error(received_bits):
    parity = sum(received_bits) [1] 2
    return parity != 0

Drag options to blanks, or click blank then click option'

A%

B//

C+

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Using floor division instead of modulo.

Checking for equality to zero instead of inequality.

The parity check uses modulo 2 to determine if the sum of bits is odd, indicating an error.

3fill in blank

hard

Fix the error in the code to correctly calculate the Hamming distance between two bit strings.

Signal Processing

def hamming_distance(bits1, bits2):
    return sum(b1 != b2 for b1, b2 in zip(bits1, [1]))

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Abits1

Bbits1[::-1]

Crange(len(bits1))

Dbits2

Attempts:

3 left

💡 Hint

Common Mistakes

Using bits1 twice instead of bits2.

Using range instead of the second bit string.

The Hamming distance compares corresponding bits from both bit strings, so we must zip bits1 and bits2.

4fill in blank

hard

Fill both blanks to create a dictionary comprehension that maps each bit string to its parity bit.

Signal Processing

parity_dict = [1]: sum([2]) % 2 for [1] in bit_strings}

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Abits

Bbit_strings

Cbit

Dbits_list

Attempts:

3 left

💡 Hint

Common Mistakes

Using different variable names inconsistently.

Using the list name instead of the loop variable.

We iterate over each bit string named 'bits' and calculate parity by summing bits in 'bit'.

5fill in blank

hard

Fill all three blanks to filter bit strings with parity bit 1 and create a list of their indices.

Signal Processing

indices = [i for i, bits in enumerate([1]) if sum(bits) [2] 2 == [3] 1]

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Abit_strings

B%

C==

D!=

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong comparison operator.

Using wrong variable name for the list.

We enumerate over bit_strings, check if sum of bits modulo 2 equals 1 to find odd parity, then collect indices.

Practice

1. What is the main purpose of error detection in data transmission?

easy

A. To find mistakes in data using extra bits

B. To increase the speed of data transmission

C. To compress data for storage

D. To encrypt data for security

Solution

1. Step 1: Understand error detection

   Error detection uses extra bits added to data to check if errors occurred during transmission.

2. Step 2: Identify the main goal

   The goal is to find mistakes, not to speed up, compress, or encrypt data.

3. Final Answer:

   To find mistakes in data using extra bits -> Option A

4. Quick Check:

   Error detection = find mistakes [OK]

Hint: Error detection finds mistakes, not speed or compression [OK]

Common Mistakes:

• Confusing error detection with encryption
• Thinking error detection speeds up data
• Mixing error detection with data compression

2. Which of the following is the correct way to represent a parity bit for even parity in a 4-bit data 1011?

easy

A. Add a 1 to make total 1s count odd

B. Add a 0 to keep total 1s count even

C. Add a 1 to keep total 1s count even

D. Add a 0 to make total 1s count odd

Solution

1. Step 1: Count 1s in data 1011

   Data bits: 1,0,1,1 have three 1s (odd count).

2. Step 2: Determine parity bit for even parity

   To make total 1s even, add 0 (no change) would keep count odd, so add 1 to make count 4 (even).

3. Final Answer:

   Add a 1 to keep total 1s count even -> Option C

4. Quick Check:

   3 ones + 1 parity = 4 (even) [OK]

Hint: Count 1s, add parity bit to make total even [OK]

Common Mistakes:

• Adding parity bit that keeps count odd
• Confusing even and odd parity rules
• Ignoring the current number of 1s

3. Given the 7-bit Hamming code 1001101, which bit position (1-indexed from left) contains the error if the parity bits check fails at positions 1 and 4?

medium

A. Position 3

B. Position 6

C. Position 7

D. Position 5

Solution

1. Step 1: Understand parity check positions

   Parity bits in Hamming code are at positions 1, 2, 4. Errors detected at parity 1 and 4 mean bits 1 and 4 parity checks fail.

2. Step 2: Calculate error position

   Add failing parity positions: 1 + 4 = 5. Error is at position 5.

3. Final Answer:

   Position 5 -> Option D

4. Quick Check:

   Sum parity errors = error position 5 [OK]

Hint: Sum failing parity bit positions to find error [OK]

Common Mistakes:

• Ignoring parity bit positions
• Adding wrong parity positions
• Counting bits from right instead of left

4. Identify the error in this parity bit calculation code snippet for odd parity:

data = '1101'
parity = data.count('1') % 2
parity_bit = 1 if parity == 0 else 0
print(parity_bit)

medium

A. Counting 1s is incorrect; should count 0s

B. Parity bit assignment is correct; no error

C. Parity bit logic is reversed; should be 0 if parity is 0

D. Data string should be converted to integer list first

Solution

1. Step 1: Understand odd parity logic

   Odd parity means total 1s including parity bit should be odd. Data '1101' has 3 ones (odd).

2. Step 2: Check code logic

   parity=3%2=1 !=0, so parity_bit=0. Total 3 ones (odd). Logic sets 1 if even count (parity=0), else 0: correct for odd parity.

3. Final Answer:

   Parity bit assignment is correct; no error -> Option B

4. Quick Check:

   3 ones + 0 parity = 3 (odd) [OK]

Hint: Odd parity bit flips when count of 1s is even [OK]

Common Mistakes:

• Reversing parity bit assignment
• Counting zeros instead of ones
• Assuming data type conversion needed

5. You receive a 7-bit Hamming code 0110011. Parity bits are at positions 1, 2, and 4. After checking parity bits, you find errors at positions 2 and 4. Which bit should you flip to correct the error?

hard

A. Bit at position 6

B. Bit at position 3

C. Bit at position 5

D. Bit at position 7

Solution

1. Step 1: Identify parity bits with errors

   Errors at parity bits 2 and 4 mean these parity checks failed.

2. Step 2: Sum parity error positions

   2 + 4 = 6, so the error is at bit position 6.

3. Step 3: Correct the error by flipping bit 6

   Flipping bit 6 fixes the error detected by parity bits 2 and 4.

4. Final Answer:

   Bit at position 6 -> Option A

5. Quick Check:

   Sum parity errors = error bit 6 [OK]

Hint: Sum parity error positions to find bit to flip [OK]

Common Mistakes:

• Ignoring parity bit positions
• Adding wrong parity positions
• Flipping wrong bit position