Problem 10

Problem 10

Perform the following multiplication in base 2: [1110101]2 · [10101]2.

Solution

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.

1110101
×10101
11110111
1110101
1110101
+1110101
100110011001

Remarks

This is an easy exercise to keep the weaker students motivated and also to get them comfortable with the whole idea of computing in different bases. Of course, this is the notation that my students have seen in primary school, you may need to convert this to the notation of your local primary schools in order to get its full familiarity effect.