Ambleweb Base Convertor
Explore the true nature of "place value" by converting numbers into binary, octal and hexadecimal and more...
For more information and lesson ideas scroll to the bottom of this page or Click Here

Number to convert:
New base:


Any normal number


Select a base from the list

 

 

 
Answer =

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All about bases...

The decimal system of numbers up to 9 has developed simply because people have ten fingers. It was natural that we have adopted this system but it does not make maths any easier than working in any other base.

A computer chip, for example has difficulty dealing with anything other than 1 and 0 because a computer chip is nothing more than a vast collection of electronic switches or transistors which can only be off or on = 0 or 1

In our normal decimal system, numbers can add up to 9 in one column - beyond that a new column has to be created. This is the key idea behind the H,T,U type place value system that we teach children. But in order for able children to really understand "place value," it must be broken down and it's purpose investigated in other bases.

BINARY - Base 2

The binary (base 2) system consists of two numbers 0 and 1 - When 1 is reached a new column is created. The "value" of each column can be seen below:

128
64
32
16
8
4
2
1
1
1
0
1
0

Using the above table you can see that the decimal number 11010 is equal to 26 in the decimal system. (16+8+2=26) - Use the base checker at the top to turn 26 into binary if you want to check.

Using binary notation is a very good exercise for Numeracy Hour since the principles can be quickly taught - also some very interesting maths can be done quickly - e.g.

To half any number - simply move the digits 1 place to the right:
101100 = 44 10110=22
(what happens if their is a fractional part - Can you make a rule?)

To double a number - simply add a zero on the end:
1111 = 15 11110 = 30

A few minutes experimenting will reveal even more ways of simplifying mathematical operations by manipulating binary notation

That is why computers are so quick at sums!!!

HEXADECIMAL - Base 16

Programmers find writing large numbers in binary tedious and difficult, so how do we write numbers that a computer can quickly understand and manipulate in a shorter form? The answer is hexadecimal:

10
f
e
d
c
b
a
9
8
7
6
5
4
3
2
1
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1

The numbers in hexadecimal go beyond 9 - substituting letters as digits for values beyond 9. Children may use hexadecimal when they program Lego Robots or define colours for Webpages - See our Webpage colour code generator to see how Hexadecimal codes are used in webpage making.

SOME NUMERACY HOUR IDEAS

"THE BINARY BRAINSTORM"
Worksheets involving Binary (base 2) notation are excellent vehicles for practicing mental arithmetic. Give the children a Binary Conversion table e.g:

128
64
32
16
8
4
2
1
1
0
0
1
0
1
1
0
1
1
0
0
0

The value of each column is used to create any other number upto 255

E.g:

37 = (32 + 4 + 1) = 100101

1011000 = (64+16+8) = 88

 

THE EARTH TO GO HEXADECIMAL
Due to the rapid growth of computer dependence, Base 16, Hexadecimal - is to replace the standard Decimal system in the future. Your class has been given the responsibility of extending the digits with new symbols instead of letters!

Have the children create the new symbols and discuss with friends the ease of identification. Use a symbolic notation system worksheet to extend the children's skills.

EARTH AND THE HEXANITES
Introduce children to the planet "Hexa." The "hexanites" are a crystalline lifeform with six sided bodies and six fingers on each of their six arms. They have formed a strong alliance with Earth but continue to have problems with our Maths. They have only ever used base 6 for all their calculations, they can use their fingers to count on but they struggle with the whole idea of 6, 7, 8 and 9, because they have never existed on "Hexa" as single digits....

Ideas:

  • Your class must demonstrate to the "Hexanites" a simple system of converting their numbers by creating a table like those above.
  • Have the children work out the values of each column in the Hexanite number system.
  • The hexanites have left an order for equipment and goods in the Hexanite Base 6 notation - have the children convert it to Decimal.
  • Invent some Hexanite coinage, and buy goods and receive change.
  • The Hexanites need some astronomical data - distances and speed etc. Can the children convert Kilometres to Hexametres?
  • etc. etc.

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