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).

(2)

Place value.

(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.

MD0058

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