# Negative binary decoder

## World's simplest binary tool

This is a free online negative binary number decoder. Just load your encoded negative binaries in the input form and they will automatically get decoded to decimal numbers according to the selected negative binary representation method. It supports one's complement, two's complement, excess binary, sign bit, and base -2 representations. There are no ads, popups or nonsense, just an awesome negative binary converter. Load a negative binary – get a negative decimal. Created for developers by developers from team Browserling.

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Negative binary decoder tool
What is a negative binary decoder?

This browser-based utility converts negative binary values to negative integer values. This is the reverse operation of encoding a negative binary that converts a negative integer to its binary representation. This tool is able to decode six negative binary representation types – two's complement, one's complement, sign bit, offset binary, negative base two, and the naive scheme. To decode a binary number, it undoes the encoding process and performs the encoding steps in the reverse order. For example, in two's complement encoding the number is first inverted and then one is added to the result but in two's complement decoding, the same is done in the reverse order – first, one is subtracted and then the result is inverted. To decode a negative one's complement value, simply the inverse is taken as encoding and decoding in one's complement is just the bit invert operation. In the sign bit representation, this tool removes the most significant bit, which indicates the sign of the number and converts this number to base ten. The offset binary method (also known as excess code or biased representation) is almost the same as the two's complement method, but it has a sign bit at the beginning. Therefore, the tool first deletes the most significant bit and then applies the two's complement method on the number. Each output decimal number in these four representations has a "-" sign automatically appended so these representations don't work with positive decimal numbers. In base minus 2 representation, the decimal number x is immediately calculated by the formula x = a

_{0}(-2)^{n}+ a_{1}(-2)^{n-1}+ … + a_{n}(-2)^{0}. The coefficients a_{0}, a_{1}, …, a_{n}are individual bits of the input binary number in base -2 representation. The last method is the easiest to decode. It's the naive method that creates negative binary numbers with the help of the "-" sign that's placed before an ordinary binary number. To decode this value, the binary number after the minus sign is converted to base ten and then the base ten number is displayed in the output together with the minus sign in front of it. Simple and easy!
Negative binary decoder examples
Click to use

Decode 2's Complement

This example decodes seven negative binaries that had previously been encoded with the two's complement method. It subtracts one from each number and then inverts the bits. Decoding the first number, we get: 001 → 000 → 111, decoding the second number, we get: 0011 → 0010 → 1101, decoding the third number, we get: 01000 → 00111 → 11000, and so on. After decoding, the obtained values are converted to base ten and a minus sign is added at the beginning of each number. The first number: 111

_{2}= -7_{10}, the second number: 1101_{2}= -13_{10}, the third number: 11000_{2}= -24_{10}, and so on.
001
0011
01000
011010
001101
0100011
0010111

-7
-13
-24
-38
-51
-93
-105

**Required options**

Decode 1's Complement

In this example, we convert six padded negative binaries in one's complement representation to negative integers in the decimal base. To decode a one's complement value, it's first bitwise inverted (all bits are flipped) and then the result is converted to base ten with a minus sign before the value. One's complement method uses leading 1's to pad negative binaries. When finding the inverse value, 1's are replaced with 0's, thus padding doesn't affect the magnitude of the binary value. Let's take a look at the first input value. It's 111100, then when it's inverted, it becomes 000011, which is 3 in base ten, and a minus sign is added in front of it, so we get -3.

111100
111010
111000
110110
110100
110010

-3
-5
-7
-9
-11
-13

**Required options**

Sign Bit Negatives

This example selects the sign bit representation method in the options. This method uses the high bit (most significant bit) to determine the sign of a value. If the high bit is 1, then it's a negative number; otherwise, it's a positive number. The input values in this example have also been prefixed with the binary prefix "0b" and padded to eight bits. To convert these values, the tool removes the binary prefix, removes padding, removes the most significant bit, and treats the remaining bits as regular binary numbers. It then converts them from the binary base to the decimal base and outputs them with a minus sign as all of them had the sign bit of 1.

0b100001011
0b100010110
0b100100001
0b100101100
0b100110111
0b101000010
0b101001101
0b101011000
0b101100011

-11
-22
-33
-44
-55
-66
-77
-88
-99

**Required options**

Biased Representation

In this example, we decode six binary values that were earlier encoded using the offset binary (biased binary) representation scheme. The utility first removes the sign bit, which in this scheme is "0" and also removes the binary subscript postfix. Then it subtracts one, inverts the number, converts it to base ten, and adds the "-" sign. We can visualize the conversion algorithm for the first number: 00111₂ → (remove the first bit and ₂ postfix) → 0111 → (subtract one) → 0110 → (invert bits) → 1001 → (convert to decimal) → -9.

00111₂
00101011₂
0000000₂
0000100111₂
00000000000₂
0010000101010₂

-9
-85
-64
-473
-1024
-3030

**Required options**

Base Minus Two

This example uses an unusual base -2 and decodes numbers to base 10. To do this, it uses the formula x = a

_{0}(-2)^{n}+ a_{1}(-2)^{n-1}+ … + a_{n}(-2)^{0}, where x is the number in base 10 and the coefficients a_{0}, a_{1}, …, a_{n}are the input bits. This formula and the bits uniquely express a negative number in base 10. Let's convert the first binary number 1101 together. We have the coefficients a_{0}= 1, a_{1}= 1, a_{2}= 0, a_{3}= 1, and when we put them in the formula, we get 1×(-2)^{3}+ 1×(-2)^{2}+ 0×(-2)^{1}+ 1×(-2)^{0}= -8 + 4 + 0 + 0 = -4. So, 1101₂ is -4₁₀.
1101
111011
1111010100
1001000111
100000110100
111110001001000101

-3
-25
-300
-445
-2060
-90555

**Required options**

Naive Numbers

In this example, we decode binary numbers that simply have a minus sign in front of them. This binary representation is the only one that humans can instantly understand. It doesn't modify the binary values and simply uses the regular "-" sign to create negative numbers. Therefore, to get a negative binary, we take the absolute binary value and add the "-" sign in front of it. If 111 is 7, then -111 is -7.

-111
-1010111
-1011111101
-1100110001111
-1101010000110001

-7
-87
-765
-6543
-54321

**Required options**

Pro tips
Master online binary tools

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://onlinebinarytools.com/decode-negative-binary

__?input__=001%0A0011%0A01000%0A011010%0A001101%0A0100011%0A0010111&representation=twos-complement
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_{2}= -3.