Question

Multiply 1101 and 0110 in binary.

Answer 1

`1101*0110=1001110`

Step-by-step 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`