Answer:
[tex]1101*0110=1001110[/tex]
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:
[tex]1101=2^{3} +2^{2} +0 +2^{0} =8+4+0+1=13[/tex]
[tex]0110=0+2^{2} +2^{1} +0 =0+4+2+0=6[/tex]
[tex]13*6=78[/tex]
[tex]1001110=2^{6} +0+0+2^{3} +2^{2} +2^{1} +0=64+0+0+8+4+2+0=78[/tex]
