← IGCSE Computer Science Paper 1

Building a parity block with a parity byte

Each byte gets a row parity bit, then a final parity byte holds the parity bit for each column. The corner bit is the parity bit of the parity bits, so it checks in both directions.

Part of: IGCSE Computer Science 0478 — 2.2 Methods of Error Detection — Module 19

Understanding Building a parity block with a parity byte in IGCSE Computer Science Paper 1

What it does: The byte has two 1s, which is already even, so the row parity bit is 0. Each byte gets its own row parity bit first. The parity byte comes after that. The corner bit is the parity bit for the parity byte (its row) and for the column of row parity bits. It follows the same parity rule as the other bits. Adding a 1 makes five 1s, which is odd. The correct byte is 11110000. A 1 is needed to make the column total two 1s, which is even.

Common mistakes: 0110100 has three 1s. With even parity the row parity bit must make the total even, so it should be 1, not 0. The row should read 0110100 1. The row parity bits come first. Each byte gets its own parity bit, and only then are the column parity bits worked out to make the parity byte. Step 1 should be: Give each byte a parity bit.

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This module's key terms are also in a printable crossword (Modules 155–164) and word search (Modules 142–164).

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Learning

Duo

When building a parity block, what is added to each data byte first?

One parity bit for the whole blockA row parity bit on the end of each byte

Matches

1111000 -> 11110001

↓

The byte already has four 1s, which is even, so the even parity bit should be 0, not 1.

Applying

Meanings

Term

parity block

Meaning

Each byte gets a row parity bit, then a final parity byte holds the parity bit for each column. The corner bit is the parity bit of the parity bits, so it checks in both directions.

Practice

10110010

Testing

Gaps

Row 1: 1011001 + parity bit = 10110010

Check Answer

Spots

21011001 0

30110100 0

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Quick Questions

1. When building a parity block, what is added to each data byte first?

A. A row parity bit on the end of each byte ✓

B. One parity bit for the whole block

Each byte gets its own row parity bit first. The parity byte comes after that.

2. How is each bit of the parity byte worked out?

A. From the bits in one row, going across a single byte

B. From the bits in one column, going down all the bytes ✓

Row parity bits check across each byte. The parity byte holds one parity bit per column.

3. Even parity: a column holds 1, 0, 1, 1. What is that column's parity bit?

A. 1 ✓

B. 0

There are three 1s, which is odd. Even parity needs an even number of 1s, so the parity bit is 1 to make four.

4. Odd parity: a column holds 1, 1, 0, 0. What is that column's parity bit?

A. 0

B. 1 ✓

There are two 1s, which is even. Odd parity needs an odd number of 1s, so the parity bit is 1 to make three.

5. Even parity: what row parity bit goes on the end of the byte 01101011?

A. 1 ✓

B. 0

The byte has five 1s, which is odd. A parity bit of 1 makes six, which is even.

Match the Pairs

1010001 -> 10100011 → A row parity bit is added to the byte. There are three 1s, so the even parity bit is 1.

Column 3: 1, 1, 1 -> 1 → This column has three 1s, so the parity byte holds a 1 for this column to make the count even.

Row parity bits are added first, one at the end of each byte (even parity) → 0110000 -> 01100000

The corner bit is the parity bit of the row parity bits, so it checks in both directions → Row parity bits 1, 0, 0 -> corner bit 1

1111000 -> 11110001 → The byte already has four 1s, which is even, so the even parity bit should be 0, not 1.

Column 4: 0, 0, 1 -> parity bit 0 → The column has one 1, which is odd, so the even parity bit should be 1, not 0.

Key Term

parity block

Each byte gets a row parity bit, then a final parity byte holds the parity bit for each column. The corner bit is the parity bit of the parity bits, so it checks in both directions.

Fill in the Blanks

1. Row 1: 1011001 + parity bit 0 = 10110010

Hint: Type the even parity bit for this row: count the 1s and decide what makes the total even.

2. Row 2: 0110100 + parity bit 1 = 01101001

Hint: Type the even parity bit for this row. Count the 1s first.

3. Column 4 holds 1, 0, 0 so its bit is 1

Hint: Type the even parity bit for this column of three bits.

4. Row parity bits are added first. Column parity bits make the parity byte.

Hint: Type the word for the extra row made from the column parity bits.

5. Parity bits down the last column: 0, 1, 0 Corner bit (even parity) = 1

Hint: Type the corner bit: the even parity bit of the three parity bits shown.

Spot the Error

Question 1

A even parity block

B 1011001 0

C 0110100 0

D 1100110 0

E 0001011 1

Line C — 0110100 has three 1s. With even parity the row parity bit must make the total even, so it should be 1, not 0. The row should read 0110100 1.

Question 2

A 1 Make the parity byte first

B 2 Column parities form a byte

C 3 Corner bit checks both ways

Line A — The row parity bits come first. Each byte gets its own parity bit, and only then are the column parity bits worked out to make the parity byte. Step 1 should be: Give each byte a parity bit.

Question 3

A Even parity, 3 rows

B Column 4 bits: 1 1 0

C Count of 1s: one

D Parity byte bit 4 is 1

Line B — The column bits are 1 0 0, which contain one 1. That is why the next line says one, and the parity byte bit 4 must be 1 to make the total even. The broken line shows two 1s.

Question 4

A even parity block

B 1010111 1

C 0111010 0

D 1101101 0

Line D — The corner bit is the parity bit of the parity byte's other bits. 1101101 has five 1s, so with even parity the corner bit must be 1, not 0. The last line should be 1101101 1.

Question 5

A odd parity block

B 0110101 1

C 1000001 0

D 1110000 0

E 1111011 1

Line C — 1000001 has two 1s. With odd parity the whole byte must have an odd number of 1s, so the parity bit must be 1, not 0. The row should be 1000001 1.

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