← IGCSE Computer Science Paper 1

Why hexadecimal is used instead of binary

A base-16 system that shortens binary. One hex digit stands for four bits, so values are shorter to read, easier to copy without mistakes and quick to convert to and from binary.

Part of: IGCSE Computer Science 0478 — 1.1 Number Systems — Module 19

Understanding Why hexadecimal is used instead of binary in IGCSE Computer Science Paper 1

What it does: Copying 2 hex characters is less error-prone than copying 8 bits where a single 0 or 1 could easily be missed. Each hex digit maps directly to a nibble (A = 1010, 5 = 0101), whereas denary needs place-value calculations. Hex is only a human-friendly way to write binary. The computer still stores bits. Two hex digits replace eight bits. One hex digit = one nibble = 4 bits. Two hex digits make 8 bits (one byte). A long string of 0s and 1s is easy to lose your place in. Hex needs far fewer characters, so mistakes are less likely.

Common mistakes: The first nibble 1101 is D and the second nibble 0110 is 6, so the hex value is D6, not 6D. The order of the nibbles must be kept. One hex digit stands for four bits, so the number of hex digits is bits // 4, not bits // 2.

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Learning
Duo
Why do programmers often write 11111111 as FF?
FF is shorter and easier to read than 11111111The computer stores FF instead of 11111111
Matches
Hex is used because computers store data as hex digits instead of binary
↓
Computers still store and process everything as binary; hex is only used by people because it is shorter and easier to read
Applying
Meanings
Term
hexadecimal
Meaning
A base-16 system that shortens binary. One hex digit stands for four bits, so values are shorter to read, easier to copy without mistakes and quick to convert to and from binary.
Practice
Binary: 11010110 (8 digits)
Testing
Gaps
1111 0000 in binary = in hex
Check Answer
Spots
3nibble2 = "0110"
4hexValue = "6D"

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Quick Questions

1. Why do programmers often write 11111111 as FF?
A. FF is shorter and easier to read than 11111111 ✓
B. The computer stores FF instead of 11111111
Hex is only a human-friendly way to write binary. The computer still stores bits. Two hex digits replace eight bits.
2. How many binary bits does ONE hexadecimal digit represent?
A. 4 bits ✓
B. 8 bits
One hex digit = one nibble = 4 bits. Two hex digits make 8 bits (one byte).
3. Which statement about copying long values is true?
A. Binary is safer to copy because it uses only two digits
B. Hex has fewer digits, so there are fewer transcription mistakes ✓
A long string of 0s and 1s is easy to lose your place in. Hex needs far fewer characters, so mistakes are less likely.
4. Which is the hex value for the 8-bit binary number 10101111?
A. FA
B. AF ✓
Split into nibbles: 1010 = A and 1111 = F, so the answer is AF. Keep the nibbles in the same order.
5. Why is converting between hex and binary easier than between denary and binary?
A. Each hex digit matches exactly one group of 4 bits ✓
B. Hex digits match the same place values as denary
Hex and binary line up in nibbles, so no long division is needed. Denary does not line up with groups of bits.

Match the Pairs

11010110 = D6 → The 8-bit binary value is written with only 2 hex digits, so it is much shorter to read and write
1111 = F → One hex digit stands for exactly four bits (a nibble)
Hex has fewer digits than binary, so people make fewer mistakes when copying it → 10111100 -> BC
Hex converts to binary easily by swapping each digit for its 4-bit group, unlike denary → A5 -> 1010 0101
Hex is used because computers store data as hex digits instead of binary → Computers still store and process everything as binary; hex is only used by people because it is shorter and easier to read
One hex digit = 8 bits, so 11110000 = F0 needs 4 hex digits → One hex digit stands for 4 bits, not 8, so 8 bits need just 2 hex digits (F0)

Key Term

hexadecimal
A base-16 system that shortens binary. One hex digit stands for four bits, so values are shorter to read, easier to copy without mistakes and quick to convert to and from binary.

Fill in the Blanks

1. 1111 0000 in binary = F0 in hex
Hint: Type the hex value for the two groups of four bits
2. One hex digit stands for 4 bits
Hint: Type how many bits one hex digit represents
3. 10110111 (8 digits) = B7 (2 digits)
Hint: Type how many hex digits are needed instead of eight binary digits
4. 0xFF = 1111 1111
Hint: Type the 4-bit binary pattern that the first F stands for
5. Hex converts to binary easier than denary
Hint: Type the number system that does not map neatly onto groups of four bits

Spot the Error

Question 1
A binary = "11010110"
B nibble1 = "1101"
C nibble2 = "0110"
D hexValue = "6D"
Line D — The first nibble 1101 is D and the second nibble 0110 is 6, so the hex value is D6, not 6D. The order of the nibbles must be kept.
Question 2
A bits = 8
B digits = bits // 2
C print(digits)
Line B — One hex digit stands for four bits, so the number of hex digits is bits // 4, not bits // 2.
Question 3
A binary = "11111111"
B hexa = "FF"
C print(len(binary)) # 8
D print(len(hexa)) # 8
Line D — FF has only 2 hex digits, so len(hexa) is 2. The 8 belongs to the binary version. This shows hex is shorter to read and write.
Question 4
A bits_per_hex_digit = 8
B digits = 16 // bits_per_hex_digit
C print(digits)
Line A — One hex digit stands for 4 bits (a nibble), not 8. The first line should be bits_per_hex_digit = 4.
Question 5
A original = "0110101111010011"
B hexa = "6BD3"
C shorter = len(hexa) > len(original)
D print(shorter)
Line C — The hex form 6BD3 has 4 digits and the binary has 16, so hex is shorter. The comparison should use < not >.

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