What is the two's complement?

The two's complement is a way to represent negative numbers in binary when the minus sign is not available. The minus sign is substituted in the two's complement representation by a digit, usually the leading one. If the leading digit is 0, the number is positive. If the leading digit is 1, the number is negative.

How do I calculate the two's complement of a number?

To calculate the two's complement of a number: If the number is negative, subtract it from the power of 2 with exponent corresponding to the number of bits of your chosen representation. Convert the number to binary. If the number was negative, add 1 to the proper position and pad with 0. If the number was positive, left-pad the result with 0 to the desired length.

What are the disadvantages of the two's complement notation?

The two's complement notation takes one number away from the binary representation of a number. This means that, using an 8-bit representation allows us to represent numbers from −27 = −128 to 27−1 = 127. If we had renounced the use of negative numbers, 8 bits would have allowed us to represent numbers from 0 to 28−1 = 255.

What is the 8-bit two's complement notation of -37?

The 8-bit two's complement representation of −37 is 110110112. To find this result: Subtract 37 from 27: 128 − 37 =91. Find the binary representation of 91: 91 = 64 + 16 + 8 + 2 + 1 = 1·26 + 0·25 + 1·24 + 1·23 + 0·22 + 1·21 + 1·20 =1011011 Place 1 in the correct position to mark that we started from a negative number: −3710 = 110110112

Two's Complement Calculator

Last updated: January 30, 2026

Key takeaway: Check this two's complement calculator if you want to find the opposite of a binary number in its two's complement representation. You can also convert a decimal value to its binary and 2's complement forms. This free Two's Complement Calculator is designed for students, teachers, and anyone who needs quick math answers — enter your values above to get instant results.

Here is the two's complement calculator (or 2's complement calculator), a fantastic tool that helps you find the opposite of any binary number and turn this two's complement to a decimal value. You have an opportunity to learn what the two's complement representation is and how to work with negative numbers in binary systems. In the text, you can also find how this two's complement converter works or how to turn any signed binary to decimal by hand.

🔎 If you only need to convert decimal to binary or vice versa, check binary converter!

How to work with negative numbers in binary? – 2's complement representation

In the binary system, all numbers are a combination of two digits, $0$ 0 or $1$ 1. Each digit corresponds to a successive power of 2, starting on the right.

For example, $12$ 12 in binary is $1100$ 1100, as $12 =$ 8+4=1⋅23+1⋅22+0⋅21+0⋅2012=8+4=1⋅23+1⋅22+0⋅21+0⋅20 (using scientific notation). The hexadecimal system is an extended version of the binary system(which uses base 16 instead of base 2). The latter is frequently used in many computer software and systems. If you want to read more, head to our decimal to hexadecimal converter.

Learning about binary leads to many natural questions: What about negative numbers in the binary system? Or how do I subtract binary numbers? As we can only use $1$ 1 to show that something is present or $0$ 0 to mean that there is a lack of that thing, there are two main approaches:

Two's complement representation, or, in other words, signed notation – the first bit tells about the sign. The convention is that a number with a leading $1$ 1 is negative, while a leading $0$ 0 denotes a positive value. In an 8-bit representation, we can write any number from -128 to 127. The name comes from the fact that a negative number is a two's complement of a positive one.
Unsigned notation – a representation that supports only positive values. Its advantage over the signed one is that, within the same 8-bit system, we can get any number from 0 up to 255.

The unsigned notation is good enough if we need to add or multiply positive numbers. But, usually, the more practical solution is to work with negative numbers as well. A useful thing about the 2's complement representation is that subtraction is equivalent to an addition of a negative number, which we can handle.

How to use two's complement calculator? Two's complement converter in practice

Whenever you want to convert a decimal number into a binary value in two's complement representation, follow these steps:

Choose the number of bits in your notation. The higher value, the broader range of numbers you can input.
Write any whole decimal within the range that appears under the Decimal to binary section.
… and that's it – the 2's complement calculator will do the rest of the work! It shows the equivalent binary number and its two's complement.

Do you want to estimate the outcome by hand? This is how two's complement calculator does it:

Choose the number of bits in the binaries representation. Let's assume we want values in the 8-bit system.
Write down your number, let's say 16. 16 in binary is $10000$ 1 0000.
Add some leading $0$ 0's so that the number has eight digits, $00010000$ 0001 0000. That's 16 in the two's complement notation.

And what about its counterpart, $- 16$ −16?

Switch all the digits to their opposite ( $0 \to$ 10→1 and $1 \to$ 01→0). In our case, $00010000 \to$ 1110 11110001 0000→1110 1111.
Add 1 to this value, $11101111 +$ 1=1111 00001110 1111+1=1111 0000.
$11110000$ 1111 0000 in the two's complement representation is $- 16$ −16 in decimal notation and is the 2's complement of $00010000$ 0001 0000.

Look, as long as you are proficient in switching digits and adding unity to a binary value, evaluating negative numbers in binary is not a big deal!

🔎 In case of adding binary numbers, you may find our binary addition calculator helpful.

Turning two's complement to decimal

Our 2's complement calculator can also work the other way around – converting any two's complement to its decimal value. Let's try to convert $10111011$ 1011 1011, a signed binary, to decimal. Two useful methods help you find the outcome:

Method 1

Convert this signed binary into a decimal, like normal, but multiply the leading digit by $- 1$ −1 instead of $1$ 1. Starting from the right:

decimal = 1 \cdot 2^{0} + 1 \cdot 2^{1} + 0 \cdot 2^{2} + 1 \cdot 2^{3} + 1 \cdot 2^{4} + 1 \cdot 2^{5} + 0 \cdot 2^{6} - 1 \cdot 2^{7} = 1 + 2 + 8 + 16 + 32 - 128 = - 69

decimal=1⋅20+1⋅21+0⋅22+1⋅23+1⋅24+1⋅25+0⋅26−1⋅27=1+2+8+16+32−128=−69

Method 2

We can see that the first digit is $1$ 1, so our number is negative. First, find its two's complement, then convert the value to a decimal, and come back to the original value:

Reverse digits, $10111011 \to$ 0100 01001011 1011→0100 0100.
Add a unity, $01000100 +$ 1=0100 01010100 0100+1=0100 0101.
Convert to a decimal (starting from the right),

decimal = + 1 \cdot 2^{0} + 0 \cdot 2^{1} + 1 \cdot 2^{2} + 0 \cdot 2^{3} 0 \cdot 2^{4} + 0 \cdot 2^{5} + 1 \cdot 2^{6} + 0 \cdot 2^{7}

decimal=+1⋅20+0⋅21+1⋅22+0⋅230⋅24+0⋅25+1⋅26+0⋅27

$decimal = 1 + 4 + 64 = 69$ decimal=1+4+64=69.
As $69$ 69 is the absolute value of our initial (negative) binary, add a minus sign in front of it.
$10111011$ 1011 1011 is $- 69$ −69 in two's complement binary notation.

Signed binary to decimal table

If you want to find any whole number in the two's complement eight-bit representation, you may find this table handy. You can see both the value and its two's complement in the same row.

If you are interested in working with the values of a different number of bits, just use our two's complement calculator to save yourself time and effort!

Decimal	Binary	Decimal	Binary
0	0000 0000
1	0000 0001	-1	1111 1111
2	0000 0010	-2	1111 1110
3	0000 0011	-3	1111 1101
4	0000 0100	-4	1111 1100
5	0000 0101	-5	1111 1011
6	0000 0110	-6	1111 1010
7	0000 0111	-7	1111 1001
8	0000 1000	-8	1111 1000
9	0000 1001	-9	1111 0111
10	0000 1010	-10	1111 0110
11	0000 1011	-11	1111 0101
12	0000 1100	-12	1111 0100
13	0000 1101	-13	1111 0011
14	0000 1110	-14	1111 0010
15	0000 1111	-15	1111 0001
16	0001 0000	-16	1111 0000
17	0001 0001	-17	1110 1111
18	0001 0010	-18	1110 1110
19	0001 0011	-19	1110 1101
20	0001 0100	-20	1110 1100
21	0001 0101	-21	1110 1011
22	0001 0110	-22	1110 1010
23	0001 0111	-23	1110 1001
24	0001 1000	-24	1110 1000
25	0001 1001	-25	1110 0111
26	0001 1010	-26	1110 0110
27	0001 1011	-27	1110 0101
28	0001 1100	-28	1110 0100
29	0001 1101	-29	1110 0011
30	0001 1110	-30	1110 0010
31	0001 1111	-31	1110 0001
32	0010 0000	-32	1110 0000
33	0010 0001	-33	1101 1111
34	0010 0010	-34	1101 1110
35	0010 0011	-35	1101 1101
36	0010 0100	-36	1101 1100
37	0010 0101	-37	1101 1011
38	0010 0110	-38	1101 1010
39	0010 0111	-39	1101 1001
40	0010 1000	-40	1101 1000
41	0010 1001	-41	1101 0111
42	0010 1010	-42	1101 0110
43	0010 1011	-43	1101 0101
44	0010 1100	-44	1101 0100
45	0010 1101	-45	1101 0011
46	0010 1110	-46	1101 0010
47	0010 1111	-47	1101 0001
48	0011 0000	-48	1101 0000
49	0011 0001	-49	1100 1111
50	0011 0010	-50	1100 1110
51	0011 0011	-51	1100 1101
52	0011 0100	-52	1100 1100
53	0011 0101	-53	1100 1011
54	0011 0110	-54	1100 1010
55	0011 0111	-55	1100 1001
56	0011 1000	-56	1100 1000
57	0011 1001	-57	1100 0111
58	0011 1010	-58	1100 0110
59	0011 1011	-59	1100 0101
60	0011 1100	-60	1100 0100
61	0011 1101	-61	1100 0011
62	0011 1110	-62	1100 0010
63	0011 1111	-63	1100 0001
64	0100 0000	-64	1100 0000
65	0100 0001	-65	1011 1111
66	0100 0010	-66	1011 1110
67	0100 0011	-67	1011 1101
68	0100 0100	-68	1011 1100
69	0100 0101	-69	1011 1011
70	0100 0110	-70	1011 1010
71	0100 0111	-71	1011 1001
72	0100 1000	-72	1011 1000
73	0100 1001	-73	1011 0111
74	0100 1010	-74	1011 0110
75	0100 1011	-75	1011 0101
76	0100 1100	-76	1011 0100
77	0100 1101	-77	1011 0011
78	0100 1110	-78	1011 0010
79	0100 1111	-79	1011 0001
80	0101 0000	-80	1011 0000
81	0101 0001	-81	1010 1111
82	0101 0010	-82	1010 1110
83	0101 0011	-83	1010 1101
84	0101 0100	-84	1010 1100
85	0101 0101	-85	1010 1011
86	0101 0110	-86	1010 1010
87	0101 0111	-87	1010 1001
88	0101 1000	-88	1010 1000
89	0101 1001	-89	1010 0111
90	0101 1010	-90	1010 0110
91	0101 1011	-91	1010 0101
92	0101 1100	-92	1010 0100
93	0101 1101	-93	1010 0011
94	0101 1110	-94	1010 0010
95	0101 1111	-95	1010 0001
96	0110 0000	-96	1010 0000
97	0110 0001	-97	1001 1111
98	0110 0010	-98	1001 1110
99	0110 0011	-99	1001 1101
100	0110 0100	-100	1001 1100
101	0110 0101	-101	1001 1011
102	0110 0110	-102	1001 1010
103	0110 0111	-103	1001 1001
104	0110 1000	-104	1001 1000
105	0110 1001	-105	1001 0111
106	0110 1010	-106	1001 0110
107	0110 1011	-107	1001 0101
108	0110 1100	-108	1001 0100
109	0110 1101	-109	1001 0011
110	0110 1110	-110	1001 0010
111	0110 1111	-111	1001 0001
112	0111 0000	-112	1001 0000
113	0111 0001	-113	1000 1111
114	0111 0010	-114	1000 1110
115	0111 0011	-115	1000 1101
116	0111 0100	-116	1000 1100
117	0111 0101	-117	1000 1011
118	0111 0110	-118	1000 1010
119	0111 0111	-119	1000 1001
120	0111 1000	-120	1000 1000
121	0111 1001	-121	1000 0111
122	0111 1010	-122	1000 0110
123	0111 1011	-123	1000 0101
124	0111 1100	-124	1000 0100
125	0111 1101	-125	1000 0011
126	0111 1110	-126	1000 0010
127	0111 1111	-127	1000 0001
		-128	1000 0000

FAQs

What is the two's complement?: The two's complement is a way to represent negative numbers in binary when the minus sign is not available. The minus sign is substituted in the two's complement representation by a digit, usually the leading one. If the leading digit is 0, the number is positive. If the leading digit is 1, the number is negative.
How do I calculate the two's complement of a number?: To calculate the two's complement of a number: If the number is negative, subtract it from the power of 2 with exponent corresponding to the number of bits of your chosen representation. Convert the number to binary. If the number was negative, add 1 to the proper position and pad with 0. If the number was positive, left-pad the result with 0 to the desired length.
What are the disadvantages of the two's complement notation?: The two's complement notation takes one number away from the binary representation of a number. This means that, using an 8-bit representation allows us to represent numbers from −27 = −128 to 27−1 = 127. If we had renounced the use of negative numbers, 8 bits would have allowed us to represent numbers from 0 to 28−1 = 255.
What is the 8-bit two's complement notation of -37?: The 8-bit two's complement representation of −37 is 110110112. To find this result: Subtract 37 from 27: 128 − 37 =91. Find the binary representation of 91: 91 = 64 + 16 + 8 + 2 + 1 = 1·26 + 0·25 + 1·24 + 1·23 + 0·22 + 1·21 + 1·20 =1011011 Place 1 in the correct position to mark that we started from a negative number: −3710 = 110110112

Two's Complement Calculator

How to work with negative numbers in binary? – 2's complement representation

How to use two's complement calculator? Two's complement converter in practice

Turning two's complement to decimal

Method 1

Method 2

Signed binary to decimal table

FAQs

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