Binary (Base 2) to Hexadecimal (Base 16) Converter
Convert binary numbers to hexadecimal.
11111111 (base 2) = FF (base 16)
Digits in base 2: 0 and 1. Digits in base 16: 0 to 9 and A to F.
How to convert Binary to Hexadecimal
Every positional number system works the same way: a digit is worth its own value times the base raised to the power of its position. In base 2 the place values, from the right, are 20 = 1, 21 = 2, 22 = 4 and so on.
Most pairs have no direct trick, so go through decimal, the base we all calculate in. First turn the base 2 number into decimal, then divide by 16 and read the remainders from the bottom up. Two short steps, and you can check the number in the middle.
Because 16 is a power of 2, there is a faster way that skips decimal. Split the bits into groups of 4 from the right, then replace each group with one base 16 digit.
The method
decimal value = each digit × its place value, all added upplace values in base 2: 1, 2, 4, 8, 16, and so ondivide by 16, keep the remainder, repeat until the quotient is 0the answer is the remainders read from last to first1 base 16 digit = 4 bitsdigits in base 2: 0 and 1digits in base 16: 0 to 9 and A to F
Worked example 1: 101101 from binary to hexadecimal
Step 1: base 2 to decimal101101 (base 2) = 1 × 25 + 1 × 23 + 1 × 22 + 1 × 20= 32 + 8 + 4 + 1= 45Step 2: decimal to base 1645 ÷ 16 = 2 remainder 13 (D)2 ÷ 16 = 0 remainder 2Read the remainders from the bottom up: 2D101101 (base 2) = 2D (base 16)
Letters stand for values from 10 up: A = 10, B = 11, C = 12 and so on. Remainders come out last digit first, which is why you read them from the bottom up. Digits that are 0 add nothing to the sum, so they are left out of the expansion.
Worked example 2: 11111111 from binary to hexadecimal
Step 1: base 2 to decimal11111111 (base 2) = 1 × 27 + 1 × 26 + 1 × 25 + 1 × 24 + 1 × 23 + 1 × 22 + 1 × 21 + 1 × 20= 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1= 255Step 2: decimal to base 16255 ÷ 16 = 15 remainder 15 (F)15 ÷ 16 = 0 remainder 15 (F)Read the remainders from the bottom up: FF11111111 (base 2) = FF (base 16)
Worked example 3: 1111101000 from binary to hexadecimal
Step 1: base 2 to decimal1111101000 (base 2) = 1 × 29 + 1 × 28 + 1 × 27 + 1 × 26 + 1 × 25 + 1 × 23= 512 + 256 + 128 + 64 + 32 + 8= 1,000Step 2: decimal to base 161,000 ÷ 16 = 62 remainder 862 ÷ 16 = 3 remainder 14 (E)3 ÷ 16 = 0 remainder 3Read the remainders from the bottom up: 3E81111101000 (base 2) = 3E8 (base 16)
Worked example 4: 10110101 with the bit-group shortcut
10110101 (base 2)Split into groups of 4 from the right: 1011 0101Replace each group with its digit: 1011 = B, 0101 = 510110101 (base 2) = B5 (base 16)
Both bases are powers of 2, so there is no need to go through decimal. Groups of 4 bits make one base 16 digit.
Need the other direction? Open the Hexadecimal to Binary converter.
Binary to Hexadecimal examples
The decimal number 255 is written 11111111 in binary and FF in hexadecimal.
| Binary | Hexadecimal | Decimal |
|---|---|---|
| 1 | 1 | 1 |
| 10 | 2 | 2 |
| 111 | 7 | 7 |
| 1000 | 8 | 8 |
| 1010 | A | 10 |
| 1111 | F | 15 |
| 10000 | 10 | 16 |
| 100000 | 20 | 32 |
| 1000000 | 40 | 64 |
| 1100100 | 64 | 100 |
| 11111111 | FF | 255 |
| 1111101000 | 3E8 | 1000 |
Where Binary to Hexadecimal comes up
Binary uses only 0 and 1, because a digital circuit has two stable states: off and on. Every number a computer stores is binary underneath. You meet it when you work with bit flags, bit masks, subnet masks and low-level debugging.
Hexadecimal (base 16) uses 0 to 9 and A to F, and each hex digit stands for exactly four bits, so one byte is always two hex digits. You see it in web colours like #FF8800, memory addresses, MAC addresses, hash values and byte dumps.
Going to a larger base packs more value into each digit, so the result is shorter. The number 255 needs 8 digits in binary and 2 in hexadecimal.
Binary to Hexadecimal FAQ
How do I convert binary to hexadecimal?
Convert to decimal first by adding up each digit times its place value, then divide that decimal number by 16 repeatedly and read the remainders from last to first. Because both bases are powers of 2, you can also skip decimal and work with groups of bits.
Which digits does binary use?
Base 2 uses the digits 0 and 1. For example, 2 is not a valid digit in base 2.
Will the hexadecimal number be longer or shorter?
Shorter. Going to a larger base packs more value into each digit, so the result is shorter. Roughly 0.25 hexadecimal digits for every binary digit. The number 255 needs 8 digits in binary and 2 in hexadecimal.
Is there a shortcut for binary to hexadecimal?
Yes. Because 16 is a power of 2, there is a faster way that skips decimal. Split the bits into groups of 4 from the right, then replace each group with one base 16 digit.
Can I convert negative numbers or fractions?
The converter handles whole numbers, and a leading minus sign works for negatives. Fractions use a different method, where you repeatedly multiply the fractional part by the new base, and they are not supported here.