110two+11two= 11011two+1010two=

Mathematics

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Answers

2 parts
1

1001two1001_{two}

2

100101two100101_{two}

Step-by-step solution

12 steps

Here are the solutions to your binary addition problems.

Part 1· 5 steps

110two+11two110_{two} + 11_{two}

  1. Align the numbers for addition.

    110two+11two\begin{array}{c} 110_{two} \\ + \quad 11_{two} \\ \hline \end{array}

  2. Add the rightmost column (0+1=10 + 1 = 1).

    110two+11two1two\begin{array}{c} 110_{two} \\ + \quad 11_{two} \\ \hline \quad \quad 1_{two} \end{array}

  3. Add the middle column (1+1=10two1 + 1 = 10_{two}).

    Write down 0 and carry over 1.

    1110two+11two01two\begin{array}{c} ^{1} \\ 110_{two} \\ + \quad 11_{two} \\ \hline \quad \quad 01_{two} \end{array}

  4. Add the leftmost column, including the carry-over (1+1=10two1 + 1 = 10_{two}).

    Write down 0 and carry over 1.

    11110two+11two001two\begin{array}{c} ^{1} \quad ^{1} \\ 110_{two} \\ + \quad 11_{two} \\ \hline \quad 001_{two} \end{array}

  5. Bring down the final carry-over.

    11110two+11two1001two\begin{array}{c} ^{1} \quad ^{1} \\ 110_{two} \\ + \quad 11_{two} \\ \hline 1001_{two} \end{array}

    The sum is 1001two\boxed{1001_{two}}.

Part 2

100101two100101_{two}

11011two+1010two11011_{two} + 1010_{two}

  1. Align the numbers for addition.

    11011two+1010two\begin{array}{c} 11011_{two} \\ + \quad 1010_{two} \\ \hline \end{array}

  2. Add the rightmost column (1+0=11 + 0 = 1).

    11011two+1010two1two\begin{array}{c} 11011_{two} \\ + \quad 1010_{two} \\ \hline \quad \quad \quad 1_{two} \end{array}

  3. Add the next column (1+1=10two1 + 1 = 10_{two}).

    Write down 0 and carry over 1.

    111011two+1010two01two\begin{array}{c} \quad \quad ^{1} \\ 11011_{two} \\ + \quad 1010_{two} \\ \hline \quad \quad \quad 01_{two} \end{array}

  4. Add the next column, including the carry-over (0+0+1=10 + 0 + 1 = 1).

    111011two+1010two101two\begin{array}{c} \quad \quad ^{1} \\ 11011_{two} \\ + \quad 1010_{two} \\ \hline \quad \quad \quad 101_{two} \end{array}

  5. Add the next column (1+1=10two1 + 1 = 10_{two}).

    Write down 0 and carry over 1.

    1111011two+1010two0101two\begin{array}{c} \quad ^{1} \quad ^{1} \\ 11011_{two} \\ + \quad 1010_{two} \\ \hline \quad \quad 0101_{two} \end{array}

  6. Add the leftmost column, including the carry-over (1+1=10two1 + 1 = 10_{two}).

    Write down 0 and carry over 1.

    11111011two+1010two00101two\begin{array}{c} ^{1} \quad ^{1} \quad ^{1} \\ 11011_{two} \\ + \quad 1010_{two} \\ \hline \quad 00101_{two} \end{array}

  7. Bring down the final carry-over.

    11111011two+1010two100101two\begin{array}{c} ^{1} \quad ^{1} \quad ^{1} \\ 11011_{two} \\ + \quad 1010_{two} \\ \hline 100101_{two} \end{array}

    The sum is 100101two\boxed{100101_{two}}.

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