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Binary Number Multiplication
⇨The four basic rules of multiplication are:
(i) 0 x 0 = 0
(ii) 1 x 0 = 0
(iii) 0 x 1 =0
(iv) 1 x 1 = 1
⇨ Multiplication in binary is exactly as it is in decimal, i.e. multiply numbers right to left and multiply each digit of 1 number to each digit of the opposite number, them sum them up. The 3 basic binary multiplication rules are also similar to decimal. Also, remember that for every left shift of digit of the multiplier, an extra zero needs to be appended to the product. This is almost like the decimal numeration system also.
⇨ Example: Now lets try multiplying 11 to 13.Binary for 11 is 1011 and that for 13 is 1101.
Binary Decimal
1 0 1 1 1 1
x 1 1 0 1 x 1 3
----------------------------
1 0 1 1 3 3
0 0 0 0 x 1 1 x
1 0 1 1 x x
1 0 1 1 x x x
-----------------------------------
1 0 0 0 1 1 1 1 1 4 3
-----------------------------------
⇨1011 x 1 (multiplier 1st column) = 1 0 1 1
⇨ 1011 x 0 (multiplier 2nd column) = 0 0 0 0 0 (one x appended at the end)
⇨ 1011 x 1 (multiplier 4's col) = 1 0 1 1 0 0 (two x appended at the end)
⇨ 1011 x 1 (multiplier 8's col) = 1 0 1 10 0 0 (three x appended at the end)
⇨ Sum up. 1011 + 00000 + 101100 + 1011000 = (1011 + 00000) + 101100) + 1011000 = (01011 + 101100) + 1011000 = 110111 + 1011000 = 10001111.So the product is 10001111.