We can multiply the binary numbers 11112 and 10112 using the same rules as decimal multiplication.



  1. First, we multiply the top number by the rightmost digit of the bottom number, just as we would in decimal.
      1111
    x 1011
  1. Since this number is 1 and any number multiplied by 1 equals itself, we can simply record the top number below.
      1111
    x 1011
      1111
  1. Now we multiply the top number by the next digit in the bottom number. Since this is the second multiplication, we use a zero as a placeholder in the least significant digit of our answer.
      1111
    x 1011
      1111
         0
  1. The second digit is 1 so we move the top number down into our answer.
      1111
    x 1011
      1111
     11110
  1. Next, we multiply by the third digit. Since this is the third multiplication, we record two zeros in the answer.
      1111
    x 1011
      1111
     11110
        00
  1. Notice that the third digit is 0. Since any number multiplied by zero is zero, we place a row of zeros as our answer.
      1111
    x 1011
      1111
     11110
    000000
  1. Now we multiply the last digit. Since this is the fourth multiplication, we record three zeros in the answer.
      1111
    x 1011
      1111
     11110
    000000
       000
  1. The last digit is 1 so we record the top number below.
      1111
    x 1011
      1111
     11110
    000000
   1111000
  1. Now we add all of our answers using the same technique as in the multiple binary addition tutorial. This gives us our answer of 101001012.
      1111
    x 1011
      1111
     11110
    000000
   1111000
  10100101

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