Converting binary to hexadecimal is one of the easiest conversions in computing – no division, no multiplication, just regrouping. Here’s the method, why it works, and plenty of examples.
The Easy Method: Group by Fours
Step 1. Starting from the right, split the binary number into groups of 4 bits.
Step 2. If the leftmost group has fewer than 4 bits, pad it with leading zeros.
Step 3. Convert each 4-bit group to its hex digit (0000=0 … 1111=F).
Step 4. Concatenate the hex digits.
That’s the entire method. It works because 16 = 2⁴ – one hex digit holds exactly 4 bits.
Worked example: 1111001010101101
Step 1-2. Group from the right:
“`
1111 0010 1010 1101
“`
(Already in clean groups of 4.)
Step 3. Convert each group:
“`
1111 → F
0010 → 2
1010 → A
1101 → D
“`
Step 4. Result: F2AD ✓
Verify: F2AD = (15×4096) + (2×256) + (10×16) + 13 = 61440 + 512 + 160 + 13 = 62125. And the binary = 32768+16384+8192+4096 + 512 + 128+32 + 8+4+1 = 62125 ✓
The 4-Bit Lookup Table
Memorize (or bookmark) these 16 mappings:
| 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 |
More Worked Examples
Example 1: 1010 (needs padding)
“`
1010 → already 4 bits → A
“`
Result: A (= 10 decimal)
Example 2: 11011 (5 bits – pad the left)
“`
11011 → 0001 1011 → 1 B
“`
Result: 1B (= 27 decimal; check: 16+11 = 27 ✓)
Example 3: 11111111 (one full byte)
“`
1111 1111 → F F
“`
Result: FF (= 255 – the max byte value)
Example 4: 1000000 (7 bits)
“`
1000000 → 0100 0000 → 4 0
“`
Result: 40 hex = 64 decimal ✓ (Pad with ONE leading zero to make 8 bits: 01000000)
Example 5: A full 32-bit value
“`
11010110101101001011001111000101
→ 1101 0110 1011 0100 1011 0011 1100 0101
→ D 6 B 4 B 3 C 5
“`
Result: D6B4B3C5
Going the Other Way: Hex to Binary
Just reverse it – expand each hex digit to 4 bits:
“`
F2AD → F=1111, 2=0010, A=1010, D=1101
→ 1111001010101101
“`
You can drop leading zeros from the very first group: `2A` → `0010 1010` → `101010`. But keep all 4 bits for the remaining groups – `2A0` is `0010 1010 0000`, not `10101000` without the middle zeros… wait, actually those are the same value. The rule: only the leftmost group may drop leading zeros.
Why This Matters
This conversion is the bridge between how computers store data (binary) and how humans read it (hex):
- Reading a hex dump: Each pair of hex digits is one byte. `48 65 6C 6C 6F` → binary → “Hello”.
- Writing bitmasks: The permission mask `111101101` is much easier to communicate as `1ED`.
- Checking work: Converting binary → hex → decimal gives you two independent paths to verify a result.
Our binary converter shows binary, hex, and decimal simultaneously – perfect for checking your group-by-fours conversions. Try pasting `1111001010101101` and confirm you get F2AD.
Common Mistakes
- Grouping from the left. Always group from the RIGHT. `11011` grouped from the left gives `1101 1` (wrong); from the right gives `1 1011` → `1B` (correct).
- Forgetting to pad. A 5-bit number needs one leading zero to complete the leftmost group.
- Dropping zeros in middle groups. In `1010 0001`, the `0001` must stay 4 bits – it’s `1`, but writing just `1` in the middle would corrupt the value.
Frequently Asked Questions
How do you convert binary to hexadecimal?
Group the binary digits into sets of 4 starting from the right, pad the leftmost group with zeros if needed, then convert each group using the 4-bit lookup (0000=0 through 1111=F).
What is 1010 in hexadecimal?
A. It’s already 4 bits: 1010 = A = decimal 10.
What is 11111111 in hex?
FF. Each group of 1111 = F, so two groups give FF = 255 decimal.
Why group by 4 and not some other number?
Because 16 = 2⁴. Each hex digit represents exactly 4 binary digits – no more, no less. Grouping by any other size wouldn’t align with hex digits. (Grouping by 3 gives octal, base 8 = 2³.)
How do I verify my binary-to-hex conversion?
Convert the hex result to decimal, and independently convert the original binary to decimal. If both give the same number, your conversion is correct. Or just paste the binary into our binary converter and compare.
