How to Design Programs: An Introduction to Computing and Programming
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Section 2
Numbers, Expressions, Simple Programs
In the beginning, people thought of computers as number crunchers. And indeed, computers are very
good at working with numbers. Since teachers start their first-graders on computing with numbers, we
start with numbers, too. Once we know how computers deal with numbers, we can develop simple
programs in no time; we just translate common sense into our programming notation. Still, even
developing such simple programs requires discipline, and so we introduce the outline of the most
fundamental design recipe and the basic programming guideline at the end of this section.
2.1
Numbers and Arithmetic
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Computing
Numbers come in many different flavors: positive and negative integers, fractions (also known as
rationals), and reals are the most widely known classes of numbers:
5
-5
2/3
17/3
#i1.4142135623731
The first is an integer, the second one a negative integer, the next two are fractions, and the last one is an
inexact representation of a real number.
Like a pocket calculator, the simplest of computers, Scheme permits programmers to add, subtract,
multiply, and divide numbers:
(+ 5 5)
(+ -5 5)
(+ 5 -5)
(- 5 5)
(* 3 4)
(/ 8 12)
The first three ask Scheme to perform additions; the last three demand a subtraction, a multiplication,
and a division. All arithmetic expressions are parenthesized and mention the operation first; the numbers
follow the operation and are separated by spaces.
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Stepper
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