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Binary subtractor

World's simplest binary tool
Free online binary difference calculator. Just load your binary values and they will automatically get subtracted from the first value. There are no ads, popups or nonsense, just an awesome binary subtractor. Load binary values – get binary difference. Created for developers by developers from team Browserling.
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Binary Representation
Represent a negative binary as an inverted binary plus one.
Represent a negative binary as an inverted binary (flip all bits).
Set leading bit to 0 for a positive binary and 1 for a negative binary.
Similar to two's complement, but with the first bit flipped.
Simply use the - sign prefix for a negative binary.
Input and Output Format
Specify the input separator.
Pad results to this length.
Adjust base indicator. (Prefix or suffix.)
Running Difference and Decimals
Show how the results are computed step by step.
Print the decimal number in parentheses for easier understanding.

What is a binary subtractor?

learn more about this tool
This tool calculates the difference of binary numbers. It takes two or more binary numbers b1, b2, b3, … and subtracts them b1 - b2 - b3 - …. Binary numbers can have any separator between them and the delimiter character can be configured in the options. The output difference is also displayed in a binary format. As in the process of subtraction the values can get negative, we have implemented several types of signed binary representations for working with negative binary values. The first type is called "Two's Complement" and it's the most popular number representation method for binary number systems. Negative integers are complements of positive integers plus one. For example, given a positive number 101₂ (which is 5 in decimal), we can calculate its negative as follows – first, invert all bits of 101₂ and get 010₂, then add 1 to this result and get 011₂. So, −5₁₀ = 011₂. Things get interesting if we need to use padding. In two's complement scheme, positive numbers are padded with the digit "0" (for example, 5₁₀ = 00000101₂) but negative numbers are padded with the digit "1" (for example, -5₁₀ = 11111011₂). The second representation method is "One's Complement". In this case, a positive number is a regular binary number as you're used to but the negative number is simply its complement (number with all bits inverted). For example, 5₁₀ = 101₂ and -5₁₀ = 010₂. The padding is also "0" for positive numbers (for example, 5₁₀ = 00000101₂) and "1" for negative numbers (for example, -5₁₀ = 11111101₂). The third encoding method is "Signed Bit Representation", also known as "Sign-magnitude Representation" or simply "Sign-and-magnitude". This method uses the most significant bit (MSB) at the beginning of the number to indicate if it's positive or negative. If the MSB is 1, then it's a negative number, if it's 0, then it's a positive number. The number itself doesn't change. For example, 5₁₀ = 0101₂ and -5₁₀ = 1101₂. The padding in this scheme is "0" for both positive and negative numbers. For example, 5₁₀ = 00000101₂ and -5₁₀ = 10000101₂. The fourth type is called "Offset Binary Representation", sometimes known as "Excess-k Code" or "Biased Representation". The key idea in this scheme is that the number -k has all bits set to zero. Usually, k is chosen to be a power of two. For example, in excess-8 (k = 8 = 23) representation the number -8 is 0000 and the number 7 (23-1) is 1111. It's very similar to two's complement method and the only difference is the leading bit. In two's complement, the number -8 is 1000 and the number 7 is 0111. In the offset binary representation the prefix bit "1" indicates a positive binary and the prefix "0" indicates a negative binary but in two's complement, it's the other way around. Here's another example with the number 5. The decimal number 5₁₀ is 1101₂ in excess-8 representation and -5₁₀ is 0011₂. With padding, 5₁₀ is 10000101₂ and -5₁₀ is 01111011₂. The last binary representation method is "Human Subtraction". In this case, the positive and negative numbers differ only in the "-" sign. For example, 5₁₀ is 101 and -5₁₀ is -101. This representation is not used in computers as computers don't have the minus sign and only have bits. In the options, you can quickly switch between these five methods and compare the results. You can customize the padding length, as well as add a binary prefix or suffix. When subtracting several numbers, you can use the option "Running Difference" to see the result at each step of calculation. Finally, for a better understanding of all these binary numbers, we have added an option that displays the decimal result in brackets after each output binary value. Simple and easy!

Binary subtractor examples

Click to use
Subtract Two Binary Numbers
In this example, we find the difference of two binary numbers 1100100 (100 in decimal) and 10100 (20 in decimal). We enter each number on a new line and adjust the separator to "\n". As a result, we get the binary value 1010000, which is 80 in decimal.
1100100 10100
1010000
Required options
These options will be used automatically if you select this example.
Simply use the - sign prefix for a negative binary.
Specify the input separator.
Pad results to this length.
Adjust base indicator. (Prefix or suffix.)
Show how the results are computed step by step.
Print the decimal number in parentheses for easier understanding.
Running Difference
In this example, we subtract three binary numbers and display each subtraction step. To better understand the results, we have activated the "Show Decimal" option as well as "Human Subtraction" method. Thus, we see that 10000₂ - 1010₂ = 110b₂ (6₁₀) and 110₂ - 1000₂ = -10b₂ (-2₁₀). The human subtraction method simply adds a minus sign before positive binary numbers to make them negative.
10000 1010 1000
10000b (16) 110b (6) -10b (-2)
Required options
These options will be used automatically if you select this example.
Simply use the - sign prefix for a negative binary.
Specify the input separator.
Pad results to this length.
Adjust base indicator. (Prefix or suffix.)
Show how the results are computed step by step.
Print the decimal number in parentheses for easier understanding.
Two's Complement Arithmetic
This example uses the two's complement signed number representation. In this encoding scheme, a negative number is the bit-inverse of the positive number plus one. The example subtracts eight values from the first one and displays partial differences on every line. It also pads positive values with zeros and negative values with ones to the length of 6 and prints the corresponding decimal values in parentheses.
1000 1 10 11 100 101 110 111 1000
001000 (8) 000111 (7) 000101 (5) 000010 (2) 111110 (-2) 111001 (-7) 110011 (-13) 101100 (-20) 100100 (-28)
Required options
These options will be used automatically if you select this example.
Represent a negative binary as an inverted binary plus one.
Specify the input separator.
Pad results to this length.
Adjust base indicator. (Prefix or suffix.)
Show how the results are computed step by step.
Print the decimal number in parentheses for easier understanding.
One's Complement Arithmetic
In this example, we subtract 1 from the number 11 (3 in decimal) eight times and print intermediate differences along the way. The differences are encoded using the one's complement arithmetic. In this numeral system, negative numbers are bit-complement of the positive numbers. After four steps, we reach the first negative number -1₁₀, which is a bit-inverse of 1 and equals 0₂. With 8-bit padding, this number is 11111110₂. Similarly, -2₁₀ is the inverse of 2₁₀ and equals 01₂ or 11111101₂ with padding.
11 1 1 1 1 1 1 1 1
00000011 (3) 00000010 (2) 00000001 (1) 00000000 (0) 11111110 (-1) 11111101 (-2) 11111100 (-3) 11111011 (-4) 11111010 (-5)
Required options
These options will be used automatically if you select this example.
Represent a negative binary as an inverted binary (flip all bits).
Specify the input separator.
Pad results to this length.
Adjust base indicator. (Prefix or suffix.)
Show how the results are computed step by step.
Print the decimal number in parentheses for easier understanding.
Sign and Magnitude Representation
This example subtracts five even numbers, using the signed magnitude representation (SMR). This encoding uses the first bit as the + or - sign indicator. If the most significant bit (MSB) is 0, then it's a + sign and the number is positive. If the MSB is 1, then it's a - sign and the number is negative. The binaries in this example are separated by the "-" character and the running difference and the display decimal value options are enabled. When calculating the third difference, the number becomes negative -4. In SMR -4 is 1100₂. As you can see, 100₂ is 4 and adding a sign bit 1 in front of it makes it 1100₂, which is -4.
110-100-10-100-110
110 (6) 10 (2) 0 (0) 1100 (-4) 11010 (-10)
Required options
These options will be used automatically if you select this example.
Set leading bit to 0 for a positive binary and 1 for a negative binary.
Specify the input separator.
Pad results to this length.
Adjust base indicator. (Prefix or suffix.)
Show how the results are computed step by step.
Print the decimal number in parentheses for easier understanding.
Biased Representation
This example subtracts a bunch of comma-separated binary values using the excess binary (biased binary) representation. In this digital encoding scheme, negative binary values are equal to inverted positive values plus one and with the first bit inverted one more time. This scheme is the same as applying two's complement and then inverting the first bit of the result. In this encoding, positive numbers start with 1 and negative numbers start with 0 but the padding is still 0 for positive numbers and 1 for negative. When using padding, its length sets the k value. In this example, padding is 4 so k is 2padding = 16. If padding is not set, then each number has the minimal power of two k that it can fit in.
1010, 1000, 110, 100, 10, 110
11010₂ (10) 10010₂ (2) 01100₂ (-4) 01000₂ (-8) 00110₂ (-10) 00000₂ (-16)
Required options
These options will be used automatically if you select this example.
Similar to two's complement, but with the first bit flipped.
Specify the input separator.
Pad results to this length.
Adjust base indicator. (Prefix or suffix.)
Show how the results are computed step by step.
Print the decimal number in parentheses for easier understanding.
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/subtract-binary-numbers?input=1100100%0A10100&input-separator=%5Cn&human=true&padding-length=0&prefix=without-prefix&running-difference=false&show-decimal=false
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Quickly convert ASCII characters to binary numbers.
Convert Binary to ASCII
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Convert Octal to Binary
Quickly convert octal numbers to binary numbers.
Convert Binary to Decimal
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Convert Decimal to Binary
Quickly convert decimal numbers to binary numbers.
Convert Binary to Hexadecimal
Quickly convert binary numbers to hexadecimal numbers.
Convert Hexadecimal to Binary
Quickly convert hexadecimal numbers to binary numbers.
Convert Octal to Binary Coded Decimal
Quickly convert octal values to BCD values.
Convert Binary Coded Decimal to Octal
Quickly convert BCD values to octal values.
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Convert Binary Coded Decimal to Decimal
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Quickly convert an IP address to a binary IP address.
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Convert an IPv6 Address to Binary
Quickly convert an IPv6 address to a binary IPv6 address.
Convert Binary to an IPv6 Address
Quickly convert a binary IPv6 address to a human readable IPv6.
Convert a String to Binary
Quickly convert a string to binary values.
Convert Binary to a String
Quickly convert binary values to a string.
Convert Binary to Gray Code
Quickly convert binary numbers to reflected binary numbers.
Convert Gray Code to Binary
Quickly convert reflected binary numbers to binary numbers.
Convert Octal to Gray Code
Quickly convert octal numbers to reflected binary numbers.
Convert Gray Code to Octal
Quickly convert reflected binary numbers to octal numbers.
Convert Decimal to Gray Code
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Convert Gray Code to Decimal
Quickly convert reflected binary numbers to decimal numbers.
Convert Hex to Gray Code
Quickly convert hexadecimal numbers to Gray code.
Convert Gray Code to Hex
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Add Binary Numbers
Quickly calculate the sum of a bunch of binary values.
Subtract Binary Numbers
Quickly calculate the difference of a bunch of binary values.
Multiply Binary Numbers
Quickly calculate the product of a bunch of binary values.
Encode a Negative Binary
Quickly convert a negative number to a binary representation.
Decode a Negative Binary
Quickly convert a negative binary number to a decimal number.
Convert Binary to Negabinary
Quickly convert base 2 numbers to base -2.
AND Binary Values
Quickly calculate bitwise AND of a bunch of binary values.
NAND Binary Values
Quickly calculate bitwise NAND of a bunch of binary values.
OR Binary Values
Quickly calculate bitwise OR of a bunch of binary values.
NOR Binary Values
Quickly calculate bitwise NOR of a bunch of binary values.
XOR Binary Values
Quickly calculate bitwise XOR of a bunch of binary values.
XNOR Binary Values
Quickly calculate bitwise XNOR of a bunch of binary values.
NOT Binary Values
Quickly calculate bitwise NOT of a bunch of binary values.
Count Number of Ones
Quickly find the number of high bits in binary values.
Count Number of Zeros
Quickly find the number of low bits in binary values.
Invert Binary Values
Quickly invert bits of binary numbers.
Reverse Binary Numbers
Quickly reverse the order of bits in binary numbers.
Convert Text to Binary
Quickly convert plain text to binary values.
Convert Binary to Text
Quickly convert binary numbers to plain text.
Shuffle Bits in Binary Numbers
Quickly randomize the order of bits in binary numbers.
Rotate Bits in Binary Numbers
Quickly rotate bits in binary numbers to the left or right.
Shift a Binary Left
Quickly shift bits of a binary number to the left.
Shift a Binary Right
Quickly shift bits of a binary number to the right.
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Convert binary numbers to ternary numbers.
Convert Ternary to Binary
Convert ternary numbers to binary numbers.
Convert Binary to Arbitrary Base
Convert binary values to any base (up to base 64).
Convert Binary to Roman Number
Convert binary numbers to Roman numerals.
Convert Roman Number to Binary
Convert Roman numerals to binary values.
Add Binary Bits
Find the sum of set bits in binary numbers.
Swap Binary Bits
Swap pairs of adjacent bits in a binary number.
Generate a Binary Sequence
Create a list of increasing of decreasing binary numbers.
Generate an Alternating Binary Sequence
Create a binary number with alternating bits.
Binary Sheffer Stroke
Calculate bitwise sheffer stroke operator of binary values.
Convert Binary to BCD
Encode every binary bit as a binary coded decimal.
Convert BCD to Binary
Decode binary coded decimals to binary bits.
Divide Binary Numbers
Perform division operation on several binary numbers.
Rotate a Binary Right
Rotate bits of a binary number to the right.
Rotate a Binary Left
Rotate bits of a binary number to the left.
Extract Bits from Binary Numbers
Extract n-th bit from a binary number.
Calculate Parity
Count parity of a binary number.
Convert EBCDIC to Binary
Convert EBCDIC characters to binary values.
Convert Binary to EBCDIC
Convert binary bits to EBCDIC symbols.
Swap Binary Endianness
Change endianness of a binary number.
Convert Little Endian Binary to Big Endian Binary
Convert a binary number from little endian to big endian.
Convert Big Endian Binary to Little Endian Binary
Convert a binary number from big endian to little endian.
Convert a Floating Point Number to Binary
Find the binary representation of a floating point number.
Convert a Binary Number to Floating Point
Decode a binary number to a floating point number.
Binarize an Image
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Convert Binary Values to a Bitmap
Convert a binary string to a bitmap image.
Convert a Bitmap to Binary Numbers
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Replace each bit with two bits in each byte.
Convert Bits to Bytes
Group bits together to create bytes.
Convert Bytes to Bits
Expand bytes into individual bits.
Split Binary Values
Split a binary number into smaller binary numbers.
Join Binary Values
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Slice Binary Values
Extract a part of a binary number.
Replace Binary Values
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Pad Binary Values
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Truncate Binary Values
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Randomly Flip Binary Bits
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Color Binary Numbers
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Create a Binary Circle
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Create a Binary Square
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Generate Random Bits
Create a sequence of random binary bits.
Generate Random Nibbles
Create a sequence of random binary nybbles.
Generate Random Bytes
Create a sequence of random binary octets.
Generate Random Words
Create a sequence of random binary words.
Generate Random Double Words
Create a sequence of random binary long words.
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Analyze Binary Data
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All conversions and calculations are done in your browser using JavaScript. We don't send a single bit about your input data to our servers. There is no server-side processing at all. We use Google Analytics and StatCounter for site usage analytics. Your IP address is saved on our web server, but it's not associated with any personally identifiable information. We don't use cookies and don't store session information in cookies. We use your browser's local storage to save tools' input. It stays on your computer.
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