world's simplest binary tool

Free online binary to negabinary converter. Just load your binary numbers and they will automatically get converted to base -2. There are no ads, popups or nonsense, just an awesome negabinary encoder. Load a binary – get a negabinary. Created for developers by developers from team Browserling.

This browser utility converts binary numbers to negabinary numbers. It takes a value in base 2 and returns this value in base -2. Let's review how to convert a base 10 number to the binary base. To find a decimal number's representations in a binary base, write it as a sum of powers of two and then copy the coefficients before the powers. The coefficients create the binary number. Let's do it for the number 6 as an example: 6 = 1×(-2)^{2} + 1×(-2)^{1} + 0×(-2)^{0}. The coefficients are 110, therefore 6_{10} = 110_{2}. The negabinary numeral system uses the same sum formula to convert a number, except instead of powers of two, it's decomposed as powers of negative two. For the number 6, it looks like this: 6 = 1×(-2)^{4} + 1×(-2)^{3} + 0×(-2)^{2} + 1×(-2)^{1} + 0×(-2)^{0}. Now, extracting the coefficients, we get 6_{10} = 11010_{-2}. The biggest advantage of the negabinary system is that it can express negative numbers without using a special sign bit or a special signed number representation, such as two's complement or offset binary (see encode negative binary tool). Base -2 uses the same decomposition formula. For example, -6 can be decomposed as 1×(-2)^{3} + 1×(-2)^{2} + 1×(-2)^{1} + 0×(-2)^{0} and from the coefficients we find that -6_{10} = 1110_{-2}. An interesting fact about the negabinary base is that positive numbers have an odd number of bits and negative ones have an even number of bits. This tool can also show the number representation formula in base -2 and print the decimal value next to the binary. To convert multiple numbers, enter each of them on a new line and use the "-" sign to work with negative binaries. Simple and easy!

Click to try

In this example, we convert four numbers from the binary base to the negabinary base. We also show their decimal values so that they were easier to understand. The second and fourth numbers in the input are negative because they start with the minus sign. In the output, there's no minus sign as it's not needed in the negabinary base because the base is made out of a sum of powers of -2 so the sign value is included in the base itself.

1001
-1101
11101
-111010001

11001 (9)
110111 (-13)
1101101 (29)
1001110011 (-465)

Expand the negabinary as

a power series of -2.

a power series of -2.

Print the negabinary value

in the decimal base 10.

in the decimal base 10.

This example finds the representation formulas for six base -2 binaries and prints the full sums. Positive numbers have an odd number of addends in the sum and negative numbers have an even number of addends. This is simply because the largest power dominates the entire sum. If the number of terms is odd, then the top power is positive and the entire sum is positive, if the number of terms is an even number, then the top power is negative and the entire sum is negative.

1
-10
11
110
-1001
1111

1×(-2)⁰
1×(-2)¹ + 0×(-2)⁰
1×(-2)² + 1×(-2)¹ + 1×(-2)⁰
1×(-2)⁴ + 1×(-2)³ + 0×(-2)² + 1×(-2)¹ + 0×(-2)⁰
1×(-2)³ + 0×(-2)² + 1×(-2)¹ + 1×(-2)⁰
1×(-2)⁴ + 0×(-2)³ + 0×(-2)² + 1×(-2)¹ + 1×(-2)⁰

Expand the negabinary as

a power series of -2.

a power series of -2.

Print the negabinary value

in the decimal base 10.

in the decimal base 10.

You can pass input to this tool via __?input__ query argument and it will automatically compute output. Here's how to type it in your browser's address bar. Click to try!

https://onlinetools.com/binary/convert-binary-to-negabinary__?input__=1001%0A-1101%0A11101%0A-111010001&show-representation-sum=false&show-decimal=true

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when the Show Full Sum option

is off.