Binary to decimal
Rewrite any whole number from base 2 to base 10, with a table of the values that come up most often.
Converter
Binary (base 2) to Decimal (base 10) at a glance
21 rows| Binary (base 2) | Decimal (base 10) |
|---|---|
| 1 bin | 1 dec |
| 2 bin | 2 dec |
| 3 bin | 3 dec |
| 4 bin | 4 dec |
| 5 bin | 5 dec |
| 6 bin | 6 dec |
| 7 bin | 7 dec |
| 8 bin | 8 dec |
| 9 bin | 9 dec |
| 10 bin | 10 dec |
| 15 bin | 15 dec |
| 20 bin | 20 dec |
| 25 bin | 25 dec |
| 30 bin | 30 dec |
| 40 bin | 40 dec |
| 50 bin | 50 dec |
| 75 bin | 75 dec |
| 100 bin | 100 dec |
| 250 bin | 250 dec |
| 500 bin | 500 dec |
| 1,000 bin | 1,000 dec |
Quick pairs
tap to loadWhy people convert binary to decimal
Computer science courses, IP subnetting exercises, and low-level programming debugging are where binary-to-decimal conversion actually gets used day to day, since computers store and process everything in binary while humans read decimal. A single byte, 8 binary digits, covers decimal values from 0 to 255, a range worth memorizing since it underlies color values, IP address octets, and basic data types across most programming languages.
Subnet masks are a concrete case of the same conversion: a mask written as 11111111.11111111.11111111.00000000 in binary, octet by octet, is exactly 255.255.255.0 in decimal, which is why anyone working through IPv4 subnetting by hand ends up converting binary octets to decimal repeatedly until the pattern becomes automatic.
Popular number base conversions
1 pagesHow the binary (base 2) to decimal (base 10) conversion works
Binary is positional notation in base 2: each digit's place, counted from the right starting at position 0, is worth a power of 2 — 1, 2, 4, 8, 16, 32, and so on — and the decimal value is the sum of each digit multiplied by its place value.
Take the 3-bit number 101: positions are worth 4, 2, 1 from left to right, so the value is 1×4 + 0×2 + 1×1 = 5.
A longer 6-bit example, 101101, uses place values 32, 16, 8, 4, 2, 1: 1×32 + 0×16 + 1×8 + 1×4 + 0×2 + 1×1 = 32 + 8 + 4 + 1 = 45.
A full byte, 11010110, uses place values 128 down to 1: 128 + 64 + 0 + 16 + 0 + 4 + 2 + 0 = 214.
A quick sanity check works because 2 is even: the rightmost binary digit alone tells you whether the decimal result is odd or even. 101 ends in 1, so 5 is odd; 11010110 ends in 0, so 214 is even — both match the full results above, and this check catches many arithmetic slips without redoing the whole sum.
The mistake specific to this pair is miscounting digit positions, especially on longer numbers: it's easy to lose track of which power of 2 a digit sits at once you pass 8 or 16 digits, or to accidentally start counting positions from 1 instead of 0, which shifts every place value by a factor of 2 and produces a result exactly double or half the correct one.
Questions
How do I convert a decimal number back to binary?
Divide repeatedly by 2 and read the remainders from last to first. For 45: 45÷2=22 r1, 22÷2=11 r0, 11÷2=5 r1, 5÷2=2 r1, 2÷2=1 r0, 1÷2=0 r1. Reading the remainders bottom-to-top gives 101101, matching the binary value above.
Why do computers use binary instead of decimal in the first place?
Digital circuits are built from switches and transistors that are most reliably read as just two states — on or off, high voltage or low voltage — so binary maps directly onto the hardware. Representing ten distinct voltage levels for decimal digits would be far less reliable than distinguishing just two.
Is there a shortcut for converting small binary numbers in my head?
Memorize the powers of two — 1, 2, 4, 8, 16, 32, 64, 128 — and simply add up the ones whose position holds a 1. For 1011, that's 8 + 2 + 1 = 11, no long multiplication needed.
What's the most common mistake when converting binary to decimal?
Miscounting the digit positions, particularly on numbers longer than a byte, or starting the position count at 1 instead of 0, which doubles or halves the final answer depending on which direction the error goes.
Why does a decimal number need so many more binary digits to write the same value?
Each binary digit only carries one bit of information versus roughly 3.32 bits for a decimal digit, so a decimal number generally needs about 3.3 times as many digits once rewritten in binary — for example, decimal 1000 needs 4 digits but requires 10 binary digits (2⁹=512, 2¹⁰=1024) to represent.
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