Page 127 - 'Blast_Into_Math

Blast into Math! Mathematical perspectives: all aour mase are melong to us

Since we are in base b =2, the only digits are 0 and 1. So, to write 100 in base 2, the digit
in the 2 place will be 1, and we write
6
6
100 =1 ∗ 2 +(100 − 64).

6
2. The next step is to do the same thing with whatever is left over when we subtract 1∗2
from 100. This is
100 − 64 =36.

So we find the largest power of 2 that is not bigger than 36. This is

5
2 =32.

3. Now we have

5
5
6
6
100 =1 ∗ 2 +36= 1 ∗ 2 +1 ∗ 2 +(36 − 2 ).
Next, we repeat the step with the remaining part 36 − 2 . We find the largest power of 2 that
5
is not bigger than 4= 36 − 2 . That’s
5

2
2 =4.

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