Convert the hexadecimal value A3 to denary. [2 marks]

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Why is hexadecimal used, and how do you convert between hexadecimal and binary?

Understand why hexadecimal notation is used and convert between hexadecimal and binary.

A focused answer to Edexcel GCSE Computer Science 2.1.6, covering why hexadecimal notation is used as a shorthand for binary and how to convert between hexadecimal, binary and denary.

Generated by Claude Opus 4.88 min answerUpdated 2026-06-02

Reviewed by: AI editorial process; not yet individually human-reviewed

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What this dot point is asking
Why hexadecimal is used
The hex-binary relationship
Converting binary to hexadecimal
Converting to and from denary
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What this dot point is asking

Edexcel wants you to explain why hexadecimal (base 16) is used in computing, and to convert between hexadecimal and binary (and to and from denary) confidently, using the fact that one hex digit equals exactly four bits.

Why hexadecimal is used

The single biggest reason Edexcel rewards is readability with fewer errors. Compare the binary $11111010$ with its hex form $\text{FA}$ : eight characters become two, so the hex is far quicker to read and far easier to copy without slipping a digit. A single mistyped bit in a long binary string is easy to miss, whereas a two-character hex value is checked at a glance, which is why technical documentation and tools display values in hex.

Hexadecimal is common wherever raw binary would be unwieldy. Colour codes in web design use it (for example #FF8800, where each pair of hex digits is the red, green and blue intensity from 0 to 255). Memory addresses are written in hex because they are long binary values. Machine-code and error dumps are shown in hex so a programmer can read them. In every case it is not that the computer uses hex internally (it still stores binary); hex is purely a convenient notation for people.

The hex-binary relationship

The conversion table for one nibble is worth knowing by heart: $0000=0$ , $0001=1$ , ..., $1001=9$ , $1010=\text{A}$ , $1011=\text{B}$ , $1100=\text{C}$ , $1101=\text{D}$ , $1110=\text{E}$ , $1111=\text{F}$ .

Converting binary to hexadecimal

Convert 10111110 to hex and 4B to binary

Convert the binary number $10111110$ to hexadecimal, then convert $\text{4B}$ from hexadecimal to binary.

Step 1: Split the binary number into 4-bit nibbles from the right

One hex digit represents exactly four bits, so we group the bits into pairs of four starting from the right. An 8-bit number splits neatly into two nibbles with no padding needed.

10111110 \rightarrow 1011 \mid 1110

Step 2: Convert each nibble to its hex digit

Each 4-bit group has a denary value, and values 10 to 15 map to the letters A to F.

$1011 = 8 + 2 + 1 = 11 = \text{B}$ and $1110 = 8 + 4 + 2 = 14 = \text{E}$ , so $10111110 = \text{BE}$ .

Step 3: Convert 4B from hex to binary by expanding each digit

For the reverse direction, replace each hex digit with its 4-bit group, keeping the left-to-right order.

$4 = 0100$ and $\text{B} = 11 = 1011$ , so $\text{4B} = 01001011$ .

Step 4: Cross-check via denary

A denary check confirms both conversions: $\text{BE} = 11 \times 16 + 14 = 176 + 14 = 190$ , and $10111110 = 128 + 32 + 16 + 8 + 4 + 2 = 190$ . The two match, so the conversion is correct.

Final answer: $10111110 = \text{BE}$ in hexadecimal; $\text{4B} = 01001011$ in binary.

Converting to and from denary

To convert hex to denary, multiply the left digit by 16 and add the right digit (for two-digit hex): $\text{2C} = 2 \times 16 + 12 = 44$ . To convert denary to hex, the easiest route at GCSE is via binary: write the denary number in binary, then group into nibbles. For example $44 = 00101100$ , which splits into $0010 = 2$ and $1100 = \text{C}$ , giving $\text{2C}$ . Going through binary avoids errors and uses the four-bits-per-digit rule you already know.

Convert denary 158 to hexadecimal via binary

Convert the denary number $158$ to hexadecimal by going through binary first.

Step 1: Write 158 in 8-bit binary using place values

Going via binary avoids errors and lets us use the four-bits-per-digit rule directly. Work out which powers of 2 add up to 158.

$158 = 128 + 16 + 8 + 4 + 2 = 10011110$

Step 2: Split the binary number into two 4-bit nibbles

Group from the right to get two nibbles.

10011110 \rightarrow 1001 \mid 1110

Step 3: Convert each nibble to a hex digit

$1001 = 8 + 1 = 9$ and $1110 = 8 + 4 + 2 = 14 = \text{E}$ , so $158 = \text{9E}$ in hexadecimal.

Step 4: Cross-check by converting back

Verify the answer: $\text{9E} = 9 \times 16 + 14 = 144 + 14 = 158$ , which matches the original number, confirming the conversion is correct.

Final answer: $158_{10} = \text{9E}_{16}$ .

Try this

Q1. Convert the hexadecimal value $\text{A}3$ to denary. [2 marks]

Cue. $10 \times 16 + 3 = 163$ .

Q2. Convert the binary number $01101001$ to hexadecimal. [2 marks]

Cue. $0110 = 6$ and $1001 = 9$ , so $69$ .

Exam-style practice questions

Practice questions written in the style of Pearson Edexcel exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

Edexcel 20232 marksConvert the binary number 11010110 into hexadecimal. Show your working.

Show worked answer →

Split the 8-bit number into two 4-bit nibbles and convert each to a hex digit.

$1101 = 13 = \text{D}$ and $0110 = 6$ . So $11010110 = \text{D6}$ in hexadecimal.

Markers reward splitting into nibbles, converting each nibble correctly (1101 to D, 0110 to 6), and writing the two hex digits in the right order. The denary check is $214 = 13 \times 16 + 6$ .

Edexcel 20223 marksExplain one reason why hexadecimal is used to represent binary values, and convert the hexadecimal value 2F into binary.

Show worked answer →

Hexadecimal is used because it is a shorter, more readable shorthand for binary: one hex digit represents exactly four bits, so a long binary string becomes far fewer characters, which is easier for people to read and write and less error-prone.

To convert 2F: $2 = 0010$ and $\text{F} = 15 = 1111$ , so $\text{2F} = 00101111$ .

Markers reward a valid reason (more compact or readable, fewer errors than long binary), and converting each hex digit to its 4-bit group in the correct order.

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Sources & how we know this

Pearson Edexcel GCSE (9-1) Computer Science (1CP2) specification — Pearson (2020)