Binary (Base 2) to Base 32 Converter
Convert binary numbers to base 32.
11111111 (base 2) = 7V (base 32)
Digits in base 2: 0 and 1. Digits in base 32: 0 to 9 and A to V.
How to convert Binary to Base 32
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 32 and read the remainders from the bottom up. Two short steps, and you can check the number in the middle.
Because 32 is a power of 2, there is a faster way that skips decimal. Split the bits into groups of 5 from the right, then replace each group with one base 32 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 32, keep the remainder, repeat until the quotient is 0the answer is the remainders read from last to first1 base 32 digit = 5 bitsdigits in base 2: 0 and 1digits in base 32: 0 to 9 and A to V
Worked example 1: 101101 from binary to base 32
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 3245 ÷ 32 = 1 remainder 13 (D)1 ÷ 32 = 0 remainder 1Read the remainders from the bottom up: 1D101101 (base 2) = 1D (base 32)
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 base 32
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 32255 ÷ 32 = 7 remainder 31 (V)7 ÷ 32 = 0 remainder 7Read the remainders from the bottom up: 7V11111111 (base 2) = 7V (base 32)
Worked example 3: 1111101000 from binary to base 32
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 321,000 ÷ 32 = 31 remainder 831 ÷ 32 = 0 remainder 31 (V)Read the remainders from the bottom up: V81111101000 (base 2) = V8 (base 32)
Worked example 4: 10110101 with the bit-group shortcut
10110101 (base 2)Pad the left with zeros and split into groups of 5: 00101 10101Replace each group with its digit: 00101 = 5, 10101 = L10110101 (base 2) = 5L (base 32)
Both bases are powers of 2, so there is no need to go through decimal. Groups of 5 bits make one base 32 digit.
Need the other direction? Open the Base 32 to Binary converter.
Binary to Base 32 examples
The decimal number 255 is written 11111111 in binary and 7V in base 32.
| Binary | Base 32 | Decimal |
|---|---|---|
| 1 | 1 | 1 |
| 10 | 2 | 2 |
| 111 | 7 | 7 |
| 1000 | 8 | 8 |
| 1010 | A | 10 |
| 1111 | F | 15 |
| 10000 | G | 16 |
| 100000 | 10 | 32 |
| 1000000 | 20 | 64 |
| 1100100 | 34 | 100 |
| 11111111 | 7V | 255 |
| 1111101000 | V8 | 1000 |
Where Binary to Base 32 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.
Base 32 here uses 0 to 9 and A to V, and each digit stands for exactly five bits. It is handy for compact IDs. The text encodings called Base32 in RFC 4648 work on bytes and use their own alphabets, so their output is not the same as converting a whole number.
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 base 32.
Binary to Base 32 FAQ
How do I convert binary to base 32?
Convert to decimal first by adding up each digit times its place value, then divide that decimal number by 32 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 base 32 number be longer or shorter?
Shorter. Going to a larger base packs more value into each digit, so the result is shorter. Roughly 0.2 base 32 digits for every binary digit. The number 255 needs 8 digits in binary and 2 in base 32.
Is there a shortcut for binary to base 32?
Yes. Because 32 is a power of 2, there is a faster way that skips decimal. Split the bits into groups of 5 from the right, then replace each group with one base 32 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.