Part One 143Question 1-3
The Hindu-Arabic system uses the numeral 0 to represent a quantity of nothing. Why is this
significant?
Answer 1-3
The numeral 0 serves as a placeholder when writing numerals to represent large numbers. It
makes arithmetic easier than it was with the Roman system, or with systems that used simple
counting. Eventually, it made higher mathematics, such as algebra, possible.
Question 1-4
What’s the difference between an “English billion” and a “U.S. billion”?
Answer 1-4
In England, the term “billion” usually refers to the quantity represented by the numeral
1,000,000,000,000. In the United States, it means the quantity represented by 1,000,000,000.
The “English billion” is called a “trillion” in the United States.
Question 1-5
What’s the difference between the decimal, binary, octal, and hexadecimal numeration
systems?
Answer 1-5
The decimal system works in base ten, where the numeral 10 represents the number of dots
in the following group:
- • • • • • • • • •
If we use decimal numerals to represent quantities, then the binary system works in base 2, the
octal system works in base 8, and the hexadecimal system works in base 16.
Question 1-6
The hexadecimal system needs some extra digits besides the usual 0 through 9 to denote num-
bers. What are these digits, and what are their decimal equivalents?
Answer 1-6
Here are the extra digits and their decimal equivalents:
- Hexadecimal A stands for decimal 10.
- Hexadecimal B stands for decimal 11.
- Hexadecimal C stands for decimal 12.
- Hexadecimal D stands for decimal 13.
- Hexadecimal E stands for decimal 14.
- Hexadecimal F stands for decimal 15.