Download PDF THE DEFINITIVE GUIDE TO HOW COMPUTERS DO MATH Featuring The Virtual DIY Calculator by Clive “MAX” Maxfield and Alvin Brown

Sinopsis

Why Do We Need to Know this Stuff?
 

The number system with which we are most familiar is the decimal system, which is based on ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. As we shall soon discover, however, it’s easier for electronic systems to work with data that is represented using the binary number system, which comprises only two digits: 0 and 1.
 

Unfortunately, it’s difficult for humans to visualize large values presented as strings of 0s and 1s. Thus, as an alternative, we often use the hexadecimal number system, which is based on sixteen digits that we represent
by using the numbers 0 through 9 and the letters A through F. 

Familiarity with the binary and hexadecimal number systems is necessary in order to truly understand how computers and calculators perform their magic. In this chapter, we will discover just enough to make us dangerous, and then we’ll return to consider number systems and representations in more detail in Chapters 4, 5, and 6.
 

Counting on Fingers and Toes
 

The first tools used as aids to calculation were almost certainly man’s own fingers. It is no coincidence, therefore, that the word “digit” is used to refer to a finger (or toe) as well as a numerical quantity. As the need grew to represent greater quantities, small stones or pebbles could be used to represent larger numbers than could fingers and toes. These had the added advantage of being able to store intermediate results for later use. Thus, it is also no coincidence that the word “calculate” is derived from the Latin word for pebble.
 

Throughout history, humans have experimented with a variety of different number systems. For example, you might use one of your thumbs to count the finger joints on the same hand (1, 2, 3 on the index finger; 4, 5, 6 on the next finger; up to 10, 11, 12 on the little finger). Based on this technique, some of our ancestors experimented with base- 12 systems. This explains why we have special words like dozen, meaning “twelve,” and gross, meaning “one hundred and forty-four” (12 × 12 = 144). The fact that we have 24 hours in a day (2 × 12) is also related to these base-12 systems.
 

Similarly, some groups used their fingers and toes for counting, so they ended up with base-20 systems. This is why we still have special

Content

1.  Why This Book Is So Cool
2. Introducing Binary and Hexadecimal Numbers
3. Computers and Calculators
4. Subroutines and Other Stuff
5. Integer Arithmetic
6. Creating an Integer Calculator
7. More Functions and Experiments
8. Interactive Laboratories
9. Installing Your DIY Calculator
10. Addressing Modes
11. Instruction Set Summary

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