Binary ↔ Decimal Converter
Convert between binary (base-2) and decimal (base-10) number systems. Enter a value in either field to see the conversion.
Binary numbers use only 0's and 1's
Standard base-10 number system (0-9 digits)
Enter a valid binary number (composed of 0s and 1s) into the Binary field, and the Decimal equivalent will appear. Or, enter a decimal number into the Decimal field, and the Binary equivalent will appear.
Example: Binary '1101' is Decimal '13'
How to use Binary ↔ Decimal Converter
- 1
Enter binary digits
Type or paste a binary number made up of 0s and 1s into the input field.
- 2
Convert to decimal
Run the conversion to instantly turn the binary value into its base-10 decimal equivalent.
- 3
Read the result
View the decimal number in the output area, ready to use or verify.
- 4
Copy the answer
Copy the decimal result to your clipboard for use in code, homework, or documents.
Converting Binary to Decimal
Two number systems, one value
Decimal is the base-10 system we use every day, built from ten digits, 0 through 9. Binary is the base-2 system computers use internally, built from just two digits, 0 and 1, each called a bit. Converting binary to decimal does not change the quantity; it only rewrites the same value in the notation people read most easily. The number eleven is 1011 in binary and 11 in decimal, and both name the identical amount.
The reason the two systems coexist is hardware. A computer's circuits have two reliable states, on and off, which map cleanly to 1 and 0, so machines work in binary. Humans, with ten fingers, settled on base 10. A converter like this one is the bridge: it takes the machine's native form and produces the human-friendly equivalent, and it can also run the reverse direction.
Positional notation and place values
Both systems are positional, meaning a digit's contribution depends on where it sits. In decimal, the columns from the right are ones, tens, hundreds, and so on — successive powers of ten. Binary works the same way but with powers of two, so the columns from the right are 1, 2, 4, 8, 16, 32, 64, 128, and upward, each column being double the one to its right.
To read a binary number, you look at each position, and wherever there is a 1 you add that column's place value; wherever there is a 0 you add nothing. The rightmost bit is the ones place (two to the power of zero), the next is the twos place (two to the power of one), then fours, eights, and so on. Summing the place values of the 1 bits gives the decimal total. That single rule is the entire conversion.
Worked example: 1011 to decimal
Take the binary number 1011 and label the columns from the right: the rightmost bit is the 1s place, then 2s, then 4s, then 8s. Reading the bits against those columns, you have a 1 in the 8s place, a 0 in the 4s place, a 1 in the 2s place, and a 1 in the 1s place.
Now add the place values wherever a 1 appears: 8 + 0 + 2 + 1. That sums to 11, so binary 1011 equals decimal 11. The single 0 contributes nothing, which is exactly why it is there — to hold the 4s column empty. Every binary-to-decimal conversion is this same addition of powers of two, no matter how long the number is.
A second example with a full byte
Try the eight-bit value 11001000, a full byte. The eight columns, from the right, carry the place values 1, 2, 4, 8, 16, 32, 64, and 128. Mark where the 1 bits fall: there is a 1 in the 128s place, a 1 in the 64s place, a 1 in the 8s place, and 0 everywhere else.
Add those up: 128 + 64 + 8 equals 200, so 11001000 is decimal 200. Working with a fixed eight-bit width is common because one byte spans 0 (00000000) to 255 (11111111). Knowing that the leftmost bit of a byte is worth 128 and the values double down to 1 on the right lets you convert most bytes quickly in your head.
Leading zeros and number length
Leading zeros never change a binary value, exactly as they do not in decimal. The numbers 1011, 01011, and 00001011 all equal decimal 11, because a 0 in a high column simply contributes nothing to the sum. Computers often pad binary to a fixed width — eight bits for a byte, sixteen or thirty-two for larger types — purely for alignment, not because the extra zeros carry meaning.
So when you paste a binary string with leading zeros, you can keep them or strip them; the decimal result is the same. The total length does set the maximum value, though: with n bits you can represent zero up to two-to-the-n minus one. Eight bits top out at 255, sixteen bits at 65535. This tool handles long strings, but very large values can exceed standard numeric precision, so for everyday bytes and integers the result is exact.
The doubling shortcut for fast conversion
There is a quick mental method that avoids writing out place values. Read the bits from left to right, starting with a running total of 0. For each bit, double the running total and then add the current bit. When you reach the end, the running total is the decimal value. This works because each step left-shifts everything you have accumulated by one binary place.
Apply it to 1011. Start at 0. First bit 1: 0 doubled is 0, plus 1 is 1. Second bit 0: 1 doubled is 2, plus 0 is 2. Third bit 1: 2 doubled is 4, plus 1 is 5. Fourth bit 1: 5 doubled is 10, plus 1 is 11. The answer is 11, matching the place-value method. The doubling trick is often faster for long numbers because you never have to recall which power of two a column represents.
Why this matters
Binary-to-decimal conversion is fundamental to learning how computers work, and it is a standard topic in computer-science courses and certification exams. Understanding that a byte is just a sum of powers of two takes the mystery out of data sizes, memory, and number ranges, and it is the prerequisite for grasping topics like bitwise operations and two's-complement integers.
It also has hands-on uses. Network engineers convert binary octets to decimal to read IP addresses and subnet masks. Programmers translate binary literals, register values, and bit flags into readable numbers while debugging. Whenever you face a string of ones and zeros and need to know the quantity it represents, this conversion is the tool, and seeing the place-value breakdown reinforces the method rather than just handing you an answer.
Frequently asked questions
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