Figure 1-8. Solution to powers of two, exercise--previous page.
(b) Thus, an one by itself is worth one because the one occupies the
place whose value is 10 or 1. Putting the one to the left of zero (a placeholder) makes
the one worth 10, as it now occupies the second place to the left, valued at 101 or 10.
Putting the one to the left of two zeros, makes it worth 100, as it occupies the third place
to the left, valued at 102 or 100. We don't go through this process consciously when
working in the decimal system, because it is familiar to us. What we are doing is adding
up the value of the places marked by any digit except 0 (and multiplying each place
value by the digit). In the example below, the digits are all is (1, 10, 100, 1000).
Figure 1-9. Place value, something we take for granted in the familiar decimal system,
determines the value of the number.
(c) Let's do a decimal number in which-the digits aren't 1s, the number
23. The 2 occupies the place valued at 101. The digit 2 x the place value, is 2 x 101 = 2
x 10 = 20. The three occupies the place valued at 100. The digit 3 x the place value, is
3 x 10 = 3 x 1 = 3.