Saturday, October 2, 2010

Multiplying by Sixteen (BASIC)

16 = 10 + 5 + 1
16 = 10 + (10 / 2) + 1

So:

x * 16 = 10x + (10x/2) + x

Example 1: 26 * 16:

26 * 16 = 260 + (260/2) + 26 = 416

Example 2: 156 * 16:

1560 + (1560/2) + 156 = 1560 + [(1500 + 60)/2] + 156
= 1560 + [750 + 30] + 156 = (1500 + 700 + 100) + (60 + 50 + 30 + 50) + 6 = 2496

Example 3: 220 * 16:

2200 + (2200/2) + 220 = 3520