Alternative Base Addition
Curriculum[edit]
Coder Merlin™ Computer Science Curriculum Data  
Unit: Numbers Experience Name: Alternative Base Addition (W1012) Knowledge and skills:
Topic areas: Positional notation Classroom time (average): 60 minutes Study time (average): 180 minutes Successful completion requires knowledge: understand positional notation; understand how numbers specified in positional notation are added Successful completion requires skills: ability to use positional notation to represent numbers in the binary, octal, decimal, and hexadecimal systems; ability to convert between representations of numbers in the binary, octal, decimal, and hexadecimal systems; ability to count by one using numbers in the binary, octal, decimal, and hexadecimal systems; ability to add together numbers in the binary, octal, decimal, and hexadecimal systems 
Addition (Decimal System)[edit]
Addition is a basic (and critical) operation. Important properties of addition include:
 Addition is commutative, meaning that the order of the operands does not matter
 Addition is associative, meaning that when we're adding more than two operands, the order that we perform the addition does not matter
 The identity element for addition, also termed the additive identity, is zero
 The operator for addition is the plus () sign
 The operands for addition are called addends
Let's review how we perform addition in the number system with which we are most familiar, the decimal system.
There are a few simple rules when adding nonnegative, whole numbers:
 Align the addends vertically, flush right. (This step ensures that the position multiplier is the same for both addends in each column.)
 If any addend has fewer digits than the addend with the maximum digits, we may place a zero in columns to the left of the existing addend. (Leading zeroes don't affect the value.)
 Starting from the rightmost column, add the two digits of the addend and the carry. Note that this means that we are adding three operands in each column. If the sum exceeds the quantity that can be represented with a single digit, carry a one to the column to the left.
 Repeat the process with the column to the left until reaching the final column.
Let's look at a few examples:
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To add we:


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To add we:


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To add we:


 Describe the general process for executing addition, regardless of base.
Addition (Octal System)[edit]
There's no need for any additional rules for the octal system. In fact, for all systems, the rules are exactly the same! But let's review the octal number line before proceeding to an example:
How would we add ?
Be sure that you fully understand the above diagram before proceeding.
[edit]
To add we:


 What special factors need to be considered when executing addition with octal numbers?
Addition (Hexadecimal System)[edit]
Let's review the hexadecimal number line before proceeding to an example. How would we add ?
Remember that in number systems with bases greater than 10, by convention, we use letters in place of digits.
Digit  Value 

A  10 
B  11 
C  12 
D  13 
E  14 
F  15 
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To add we:


 What special factors need to be considered when executing addition with hexadecimal numbers?
Addition (Binary System)[edit]
Let's jump right in to an example:
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To add we:


 What special factors need to be considered when executing addition with binary numbers?
Key Concepts[edit]
 Addition is a basic (and critical) operation
 Addition is commutative
 Addition is associative
 The identity element for addition, also termed the additive identity, is zero
 The operator for addition is the "+" sign
 The operands for addition are called addends
 When adding nonnegative, whole numbers:
 Align the addends vertically, flush right
 If any addend has fewer digits than the addend with the maximum digits, we may place a zero in columns to the left of the existing addend
 Starting from the rightmost column, add the two digits of the addend and the carry. If the sum exceeds the quantity that can be represented with a single digit, carry a one to the column to the left.
 Repeat the process with the column to the left until reaching the final column
Exercises[edit]
 J1012 Create a journal and answer all questions in this experience. Be sure to:
 edit your journal using emacs within your ~/Journals directory
 properly name your journal as J1012.txt
 include all sections of the journal, properly formatted
 push your changes to GitHub
 properly tag your journal as J1012.Final
 push your tag to GitHub
 M101210 Complete Merlin Mission Manager Mission M101210.
References[edit]
 Addition (Wikipedia)
Experience Metadata
Experience ID  W1012 

Unit  Numbers 
Knowledge and skills  §10.311 §10.312 §10.313 
Topic areas  Positional notation 
Classroom time  60 minutes 
Study time  3 hours180 minutes <br /> 
Acquired knowledge  understand positional notation understand how numbers specified in positional notation are added 
Acquired skill  ability to use positional notation to represent numbers in the binary, octal, decimal, and hexadecimal systems ability to convert between representations of numbers in the binary, octal, decimal, and hexadecimal systems ability to count by one using numbers in the binary, octal, decimal, and hexadecimal systems ability to add together numbers in the binary, octal, decimal, and hexadecimal systems 
Additional categories 