Two’s Complement of 10110112 | AI Research

Two’s Complement of $1011011_2$

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Nov 4, 2026

To find the two’s complement of a binary number, the standard procedure is: [bitwise inversion]{def="Flipping each bit (0↔1)} then add 1; the result represents the negation under a fixed bit-width. This course section demonstrates the computation for $1011011_2$ (a 7-bit value).

Note: Two’s complement is defined with respect to an $n$ -bit width. Here, we treat $1011011$ as exactly 7 bits, since no other width is specified.

Two's Complement (Inverting Bits and Adding 1)

Key concepts used here:

two’s complement
bit-width
bitwise inversion
LSB

Because the bit-width controls the interpretation and overflow behavior, we compute the two’s complement using the same 7 bits as the given number.

Compute the two’s complement of $1011011$

1
Step 1
Use 7 bits because the input has 7 digits: $n=7$ .
2
Step 2
Change $1\to 0$ and $0\to 1$ : $1011011 \rightarrow 0100100$ .
3
Step 3
Compute $0100100 + 1 = 0100101$ .
4
Step 4
Therefore, the two’s complement of $1011011_2$ is $0100101_2$ .

We can also verify the negation property in 7 bits: $1011011_2 + 0100101_2 = 10000000_2$ The sum equals $2^7$ , which becomes $0000000_2$ when only 7 bits are kept—consistent with two’s complement modulo arithmetic for $n=7$ .

Pro Tip: Don’t guess the bit-width

If a question gives a binary string with no width, use its length as $n$ . Changing $n$ changes the two’s complement result.

Overflow / carry matters

When you add the final $+1$ , you may get a carry out of the MSB; with fixed $n$ bits, that carry is dropped (mod $2^n$ ).

Bit transformation from $1011011$ to its two’s complement

Shows each stage aligned per bit position (MSB → LSB).

Common checks and extensions

Two’s Complement Quick Deck

1 / 4

Question · Term

What is the standard method to compute two’s complement of a binary number?

Click to reveal

Answer · Definition

Invert all bits, then add 1 (for a fixed bit-width $n$ ).

Knowledge Check

Question 1 of 4

Q1Single choice

What is the two’s complement of $1011011_2$ (using 7 bits)?

0100101_2

0100100_2

1010101_2

1100111_2

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Two’s Complement of 101101121011011_210110112​