← IGCSE Computer Science Paper 1

Converting hexadecimal to binary using nibbles

Hex to binary: replace each hex digit with its 4-bit nibble, keeping leading zeros, then join the groups. A is 1010 and 3 is 0011, so A3 is 10100011.

Part of: IGCSE Computer Science 0478 — 1.1 Number Systems — Module 18

Understanding Converting hexadecimal to binary using nibbles in IGCSE Computer Science Paper 1

What it does: The digit 2 is 10 in binary but is padded with leading zeros to make the 4-bit nibble 0010. 3 becomes 0011 and F becomes 1111, and joining them gives 00111111. A is 1010 and 3 is 0011. The leading zeros in 0011 must be kept, so A3 is 1010 0011. Each hex digit stands for 4 bits. Two hex digits make 8 bits, which is one byte. B is 11 in denary, which is 8 + 2 + 1 = 1011. 1101 is 13, which is D. Keep the leading zero inside the nibble. 5 is 0101, which is 4 bits.

Common mistakes: Each hex digit must be written as a full 4-bit nibble, so the leading zeros must be kept. 3 should be 0011. One hex digit is always converted to 4 bits (a nibble), not 8 bits. The first line should say 4 bits.

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This module's key terms are also in a printable crossword (Modules 18–27) and word search (Modules 3–27).

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Learning
Duo
Which is the correct binary for hex A3?
1010 111010 0011
Matches
7 = 111
↓
The leading zero was dropped, so only 3 bits are written. The nibble should be 0111.
Applying
Meanings
Term
A3 = 1010 0011
Meaning
Hex to binary: replace each hex digit with its 4-bit nibble, keeping leading zeros, then join the groups. A is 1010 and 3 is 0011, so A3 is 10100011.
Practice
A = 1010
Testing
Gaps
3 =
Check Answer
Spots
2A = 1010
33 = 11

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Quick Questions

1. Which is the correct binary for hex A3?
A. 1010 11
B. 1010 0011 ✓
A is 1010 and 3 is 0011. The leading zeros in 0011 must be kept, so A3 is 1010 0011.
2. How many bits does each hex digit become?
A. 4 bits (a nibble) ✓
B. 8 bits (a byte)
Each hex digit stands for 4 bits. Two hex digits make 8 bits, which is one byte.
3. Which is hex digit 3 written as a full nibble?
A. 0011 ✓
B. 11
Always write 4 bits for each digit. 3 is 0011, not 11.
4. Which is the correct binary for hex 2F?
A. 10 1111
B. 0010 1111 ✓
2 is 0010 and F is 1111. Dropping the leading zeros of 0010 breaks the nibble pattern.
5. Which nibble is hex digit B?
A. 1011 ✓
B. 1101
B is 11 in denary, which is 8 + 2 + 1 = 1011. 1101 is 13, which is D.

Match the Pairs

A3 = 1010 0011 → Replace A with 1010 and 3 with 0011, then join the two nibbles to get 10100011
5 = 0101 → A single hex digit is written as 4 bits, so the leading zero is kept
Always write 4 bits for each hex digit, even when the digit is small → 2 = 0010
Convert each hex digit separately, then join the nibbles to make the full binary number → 3F = 0011 1111
7 = 111 → The leading zero was dropped, so only 3 bits are written. The nibble should be 0111.
B4 = 1011 100 → The nibble for 4 has only 3 bits because its leading zeros were left out. It should be 0100, so B4 = 1011 0100.

Key Term

A3 = 1010 0011
Hex to binary: replace each hex digit with its 4-bit nibble, keeping leading zeros, then join the groups. A is 1010 and 3 is 0011, so A3 is 10100011.

Fill in the Blanks

1. A = 1010 3 = 0011
Hint: Type the 4-bit nibble for the hex digit 3, keeping its leading zeros.
2. Each hex digit becomes 4 bits
Hint: Type how many bits make up one nibble.
3. 5 = 0101
Hint: Type the leading zero that keeps this nibble at 4 bits.
4. 2C = 0010 1100
Hint: Type the nibble for the second hex digit, C (denary 12).
5. B7 = 1011 0111
Hint: Type the hex digit whose nibble is the first group of bits.

Spot the Error

Question 1
A Hex: A3
B A = 1010
C 3 = 11
D Binary: 1010 0011
Line C — Each hex digit must be written as a full 4-bit nibble, so the leading zeros must be kept. 3 should be 0011.
Question 2
A Each hex digit = 8 bits
B 7 = 0111
C C = 1100
D Binary: 0111 1100
Line A — One hex digit is always converted to 4 bits (a nibble), not 8 bits. The first line should say 4 bits.
Question 3
A Hex: 5B
B 5 = 0101
C B = 1101
D Binary: 0101 1011
Line C — B is 11 in denary, which is 1011 in binary. 1101 is the nibble for D.
Question 4
A Hex: 1E
B 1 = 1000
C E = 1110
D Binary: 0001 1110
Line B — 1 in 4-bit binary is 0001. 1000 is the nibble for 8.
Question 5
A Hex: 9C
B 9 = 1010
C C = 1100
D Join: 1001 1100
Line B — 9 is 8 + 1, so its nibble is 1001. 1010 is the nibble for A.

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