Perform the following multiplication in base 2: [1110101]_{2} · [10101]_{2}.
The default arithmetic method that students have seen for this in primary school (but in base 10), is to split this product up as 10000 · 1110101 + 100 · 1110101 + 1 · 1110101. One can do exactly the same in binary, as long as one keeps in mind that 1 + 1 = 10, 1 + 1 + 1 = 11, 1 + 1 + 1 + 1 = 100, etc. Hence, this can be computed as follows, where the yellow numbers denote the carry part.
1 | 1 | 1 | 0 | 1 | 0 | 1 | ||||||
× | 1 | 0 | 1 | 0 | 1 | |||||||
1 | 1 | 1 | 10 | 1 | 1 | 1 | ||||||
1 | 1 | 1 | 0 | 1 | 0 | 1 | ||||||
1 | 1 | 1 | 0 | 1 | 0 | 1 | ||||||
+ | 1 | 1 | 1 | 0 | 1 | 0 | 1 | |||||
1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 |