Question

Multiply 1101 and 0110 in binary.

Answer 1

Answer:

$1101*0110=1001110$

Explanation:

First, multiply like if you were multiplying normally, but keep in mind this:

1*0=0

0*0=0

0*1=0

1*1=1

You should get this result:

          1 1 0 1

         0 1 1 0 x

-------------------------

         0 0 0 0

      1  1  0  1  0

   1  1  0  1  0 0    

0 0 0 0 0  0 0

Now sum these terms:

        0 0 0 0

     1  1  0  1  0

  1  1  0  1  0 0    +

0 0 0 0 0  0 0

-------------------------

The first column, from the right:

0+0+0+0=0

The second column, from the right:

0+1+0+0=1

The third column, from the right:

0+0+1+0=1

The fourth column, from the right:

1+1+0=2,

2 in binary is 0010, so we put 0 and we carry the 1

The fith column from the right:

(because we carried the 1 from the previous sum)

1+1+0=2, so the same, we put 0 and we carry the 1

And finally the sixth column, from the right:

(because we carried the 1 from the previous sum)

1+0=1

So:

          1 1 0 1

         0 1 1 0 x

-------------------------

        0 0 0 0

     1  1  0  1  0

  1  1  0  1  0 0    +

0 0 0 0 0  0 0

-------------------------

1  0 0  1  1  1  0

Let's verify the results:

$1101=2^{3} +2^{2} +0 +2^{0} =8+4+0+1=13$

$0110=0+2^{2} +2^{1} +0 =0+4+2+0=6$

$13*6=78$

$1001110=2^{6} +0+0+2^{3} +2^{2} +2^{1} +0=64+0+0+8+4+2+0=78$