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Add 1101base2, 10111base2, and 111base2

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asked Mar 24, 2013 in BASIC MATH by Afeez Novice

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1101 subscript 2 space equal 1 cross times 2 to the power of 0 plus 0 cross times 2 to the power of 1 plus 1 cross times 2 to the power of 2 plus 1 cross times 2 to the power of 3

We can change base two to base ten

1101 subscript 2 space equal space 1 cross times 1 plus space 0 cross times 2 plus 1 cross times 4 plus 1 cross times 8

1101 subscript 2 space equal space 1 plus space 0 plus 4 plus 8

1101 subscript 2 space equal space 1 plus space 4 plus 8

1101 subscript 2 space equal space 5 plus 8

1101 subscript 2 space equal space 13

10111 subscript 2 space equal space 1 cross times 2 to the power of 0 plus 1 cross times 2 to the power of 1 plus 1 cross times 2 to the power of 2 plus 0 cross times 2 to the power of 3 plus 1 cross times 2 to the power of 4

10111 subscript 2 space equal space 1 cross times 1 plus 1 cross times 2 plus 1 cross times 4 plus 0 cross times 8 plus 1 cross times 16

10111 subscript 2 space equal space 1 plus 2 plus 4 plus 0 plus 16

10111 subscript 2 space equal space 23

111 subscript 2 space equal space 1 cross times 2 to the power of 0 plus 1 cross times 2 to the power of 1 plus 1 cross times 2 to the power of 2

111 subscript 2 space equal space 1 cross times 1 plus 1 cross times 2 plus 1 cross times 4

111 subscript 2 space equal space 1 plus 2 plus 4

111 subscript 2 space equal space 7

1101 subscript 2 plus 10111 subscript 2 plus 111 subscript 2 space equal 13 space plus space 23 space plus space 7

1101 subscript 2 plus 10111 subscript 2 plus 111 subscript 2 space equal 43

43 subscript 10 equal 101011 subscript 2

answered Mar 27, 2013 by diane Scholar
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image

Step - 1

Converting binary numbers to the corresponding base - ten number.

image

image

image

Step - 2

Convert image  to the corresponding binary number.

Divide repeatedly by 2.

      R0

    ___

2 ) 2  R1

   ___

2 ) 5  R0

  ____

2 ) 10 R1

  ____

2 ) 21 R1

   ____

2 ) 43

 These remainders tell me what the binary number is,write the numbers from around the out side of the division, starting on top and wrapping my way around and down on the right hand side.

image Converts to image.

Therfore image

answered Jul 2, 2014 by david Expert

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