Figure 1-10. Determining value. Multiply each digit (except 0) by the value of
its place. Then add the subtotals.
(d) Can you "explain" the number 506? Remember, multiply each digit
by the value of the place it occupies, then add. Use the explanation of the number 23 in
the previous paragraph as your model.
Figure 1-11. Explain a decimal number exercise.
c. Converting Binary to Decimal.
(1) Symbols in a number system. The decimal or base ten system consists
of ten symbols: One through nine, plus zero. The binary or base two system consists
of two symbols: One and zero. The highest symbol in a number system will always be
one less than the base. For example, in base eight, which has eight symbols (1-7), the
highest is seven. What would the highest symbol in base nine be? You were right if
you said eight (0-8).
(a) Earlier, we said that in the decimal system each position to the left
of the decimal represented an increased power of ten. Similarly, in the binary system,
each position to the left of the decimal represents an increased power of two. In the
base three system, each position to the left of the decimal represents an increased
power of what number? You were right if you said: an increased power of three.