Steps in Constructing Modular Arithmetic Addition Tables

Step 1:

Define the Set in the Given Modulus.

Set of values used in:

• mod 2 are {0, 1}
• mod 3 are {0, 1, 2}
• mod 4 are {0, 1, 2, 3}
• mod 5 are {0, 1, 2, 3, 4}
• mod 6 are {0, 1, 2, 3, 4, 5}.

Step 2:

Using the defined set, construct the table.

Example: Draw an Addition Table for mod 5

Set of values used in mod 5 are {0, 1, 2, 3, 4}

The table will contain six rows and six columns. This is made up of the five values used (0, 1, 2, 3, 4} and the sign of the operation we are going to perform.

When constructing an addition table use this sign: ⊕

Place the sign in the first cell and the set of values in the remaining cells (on the first row and first column) as shown below.

Step 3:

Fill out the table, by performing the operation in the given modulus.