Computer Mathematics

1 + 1 = 10

Computer Number

Bases

William R. Parks, B.S., M.S., Ed.M.

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ALSO BY WILLIAM R. PARKS

1 + 1 = 1 An Introduction to Boolean Algebra

and Switching Circuits

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https://www.createspace.com/4694875

Cover

The four operations of arithmetic are displayed on the cover:

addition, subtraction, multiplication and division. The arithmetic

logic unit of a computer can calculate any of these four basic

operations of arithmetic.

Copyright © 2012 by William R. Parks

www.wrparks.com

Introduction

1 + 1 = 10 Introduction to Computer Number Bases was originally published

by Williamsville Publishing Company as part of their popular Tape ‘n Text

Computer Math Series. It has been expanded and republished as Volume 1 in

this new series. This paperback is intended for classroom teachers, students

and as a reference for libraries.

In arithmetic 1 + 1 equals 2. However, in the base two computer number

system 1 + 1 equals 10. In this context “10” does not represent the quantity

“ten.” It stands for the quantity “two” in the base two number system.

An explanation of this base two number system will be covered in detail in

the text. “Binary number system” is another name for this system of counting

because it utilizes only two symbols “0” and “1.”

The reason why this base two numeral system is used in computer

arithmetic/logic units for performing arithmetic operations is because there are

two states in computer electrical circuits. They are high and low voltage

states. The higher voltage state represents 1 and the lower voltage state

represents 0.

Knowledge of the base two number system of counting is required in our

modern world in order to understand how computers are designed and operate

at the most basic levels. In fact, many computer based devices today such as

mobile phones utilize the base two number system in their digital circuitry.

The invention of the binary number system took place many years before

computers were invented. In 1679, a famous and talented

mathematician, Gottfried Leibniz, wrote an article, Explication de

l'Arithmétique Binaire (Explanation of Binary Arithmetic) which explains the

base two number system.

However, before we introduce the base two number system, it is helpful to

review basic concepts of our popular base ten number system which is called

the decimal number system of counting used in performing everyday

arithmetic calculations. After examining in detail the decimal system, we will

then study the base two system.

Working with the binary number system is difficult when representing large

numbers. A large number in binary is represented by a rather long string of

ones and zeroes. To make binary numbers easier to understand we will

introduce the base 8 or octal number system and also the base 16 or

hexadecimal number system..

There is an easy procedure for converting binary numbers to octal or

hexadecimal numbers by grouping binary digits in sets of threes or fours. The

procedure to do this will be explained in detail.

In this “Computer Mathematics Series” new information is presented in short

sections with immediate testing. This form of personalized instruction is often

used in on-line Internet based courses for distance learning. A small amount

of information is presented in each section before advancing to the next

section. Exercises are listed after several sections followed by an answer key.

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Order the paperback edition of Computer Number Bases

from: https://www.createspace.com/4047364

List Price: $5.95

Also by William R. Parks

1 + 1 = 1 An Introduction to Boolean Algebra

and Switching Circuits

Order the paperback edition from:

https://www.createspace.com/4694875

List Price: $5.95

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List Price: $2.99

Thank you, William R. Parks, http://www.wrparks.com