Binary to Hexadecimal: The Fastest Method for Computer Science Students
If you already understand binary place values, this lesson is about speed and accuracy. It focuses on one thing only: converting between binary and hexadecimal using the grouping method, so you can stop routing every conversion through denary.
Many students convert binary to hexadecimal by first turning the binary into denary, then turning the denary into hex. It works, but it is slow and it introduces two chances to make a mistake instead of one. There is a much cleaner route.
By the end of this lesson, you will be able to:
Why four bits?
Hexadecimal is base-16. It uses sixteen symbols: the digits 0–9 and then the letters A–F to stand for the values ten to fifteen, because there are no single digits for those in our normal counting.
Four binary bits can represent exactly sixteen different values, from 0000 to 1111 — and sixteen is precisely the number of hex symbols. That is not a coincidence; it is the reason the two systems fit together so neatly. A group of four bits (a “nibble”) maps onto one hex digit, every time.
The mapping you should know
This is the whole conversion table. Learn it, or be able to rebuild it quickly from binary place values 8-4-2-1.
| Binary | Hex | Binary | Hex |
|---|---|---|---|
0000 | 0 | 1000 | 8 |
0001 | 1 | 1001 | 9 |
0010 | 2 | 1010 | A |
0011 | 3 | 1011 | B |
0100 | 4 | 1100 | C |
0101 | 5 | 1101 | D |
0110 | 6 | 1110 | E |
0111 | 7 | 1111 | F |
Method: Binary → Hexadecimal
Take the binary number 11010110.
Step 1 — split into groups of four, starting from the right:
Step 2 — convert each group using the map:
1101= D0110= 6
Result:
No denary in sight. Two nibbles, two hex digits, done.
Method: Hexadecimal → Binary
This is simply the reverse. Take the hex value 3A and replace each digit with its four bits.
3= 0011A= 1010
Result:
Write the bits in order, keep every group at four digits, and the answer assembles itself.
The important case: padding
Sometimes a binary number does not divide neatly into groups of four. When that happens, pad the left-hand side with zeros until it does.
Take 101101. That is six bits — not a multiple of four. Add two zeros on the left:
Padding on the left never changes the value, exactly as writing 7 as 07 does not change seven. Padding on the right would change it, so always pad the left.
1010 as “one thousand and ten”. It is binary: 1010 = 8 + 2 = 10 in denary, which is A in hexadecimal. If you catch yourself reading columns as thousands and hundreds, stop and use the 8-4-2-1 place values.Why hexadecimal is useful
Hexadecimal gives humans a shorter, more manageable way to write long binary values, while keeping an easy conversion relationship with binary. Eight bits become just two hex digits, which are far quicker to read and copy without error.
You will meet it in contexts such as:
- memory addresses,
- colour values,
- and machine-level data or debugging.
Retrieval Section
Try these, then reveal the answers. Three each way.
Binary → Hex: (1) 10011100 (2) 11110001 (3) 101010
Hex → Binary: (4) 7F (5) C4 (6) 2B
Check the answers
1. 1001 1100 = 9C. 2. 1111 0001 = F1. 3. pad to 0010 1010 = 2A.
4. 7 = 0111, F = 1111 → 01111111. 5. C = 1100, 4 = 0100 → 11000100. 6. 2 = 0010, B = 1011 → 00101011.
Why this beats going through denary
It is worth seeing exactly what the grouping method saves you. The long way takes 11010110, adds up the place values to get 214 in denary, then divides and finds remainders to reach D6 — three separate operations, each a chance to slip. The grouping method splits the same number into 1101 and 0110 and reads two hex digits straight off the map. One step, one place to look, far fewer errors. The more digits the number has, the bigger the saving becomes.
Final Summary
Core fact
One hex digit = exactly four binary bits.
Binary → Hex
Group in fours from the right, convert each nibble.
Hex → Binary
Replace each hex digit with its four bits, in order.
Padding
Short final group? Pad the left with zeros.