NUMBER SYSTEMS
Maths Workshop
 
3. CHANGING BASE

The principle of relative value:

The value of each figure of a number depends on its position.

For example: in the number 252 the first 2 and last 2 do not represent the same value. The first represents two hundred and the last two.
          3.1 Changing from base n to base 10

The principle of relative value is used and each position represents a power of the base. For example:

1B027(16 = 7 + 2 · 16 + 0 · 162 + 11 ·163 + 1 · 164 =  110631
EXERCISE 3:

Express the following numbers in base 10: 35(7 , 1002(5 , ABC(20 

You can check the first two answers in the window on the previous page.
          3.2 Changing from base 10 to base n

Look carefully at the steps explained in the following window.

Use the arrows to go on to the next step

STEP 1:

Choose a decimal number and base.

STEP 2:

Divide the decimal number by the base.

STEP 3:

As long as the quotient is not 0 keep dividing the last quotient into the base.

STEP 4:

Look at the remainders of all the divisions that have been made.

STEP 5:

When we express the decimal number in the base we have chosen the remainders are placed in reverse order (i.e. the last number first, going from left to right.)
EXERCISE 4:

a) Express the decimal 4752 in base 6 and base 20.

b) Express the number 20531(6 in base 4.

c) Si ves las siguientes operaciones, ¿qué dirías? (Yo no diría que están mal).

What do you think of the following calculations? (I would say that they are not wrong).

1 1 1 1 9 6 8
+  1 0 1 0 +  3 9 4

1 1 0 0 1

1 0 2 C

d) If you had to work in a different base to base 10 which one would you choose? Why? (Write down the advantages and disadvantages of the base you have chosen). Which is the best base to work in?
  Índice de unidad   Aprende a contar   ¿Cómo ganar?  
           
  Juan Simón Santamaría
 
Spanish Ministry of Education. Year 2002
 
 

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