The decimal number system
Best known positional number representation:
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Example: (high school stuff)
423
3 is in ones position (= 3 x 100)
2 is in tens position (= 2 x 101)
4 is in tens position (= 4 x 102)
423
^^^
|||
||+--- value = 3 x 1 = 3
|+---- value = 2 x 10 = 20
+----- value = 4 x 100 = 400 +
---------
represented value = 423
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The decimal number system
What does it really mean:
423
3 represents this value: •••
2 represents this value: ••
4 represents this value: ••••
3 is in ones position (= ••• x 100)
2 is in tens position (= •• x 101)
4 is in hundreds position (= •••• x 102)
423
^^^
|||
||+--- value = •••
|+---- value = •• •• •• •• •• •• •• •• •• •• (x 10)
+---- value = •••• •••• (........) •••• (x 100)
---------------------------------------
Add up all the dots: 423 dots !!
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The decimal number system as
a representation system for
numerical values
illustrated
The decimal number system is a representation system for (unsigned) numerical values:
The binary number system
The computer (due to electrical switch as memory cell) uses:
|
Example:
1011 = value expressed in decimal system ?
1011
^^^^
||||
|||+--- value = 1 x 20 = 1
||+---- value = 1 x 21 = 2
|+----- value = 0 x 22 = 0
+------ value = 1 x 23 = 8 +
-------
value expressed in decimal = 11(10)
|
The binary number system
What does it really mean:
1011
1 represents this value: •
0 represents this value: (empty)
1011
^^^^
||||
|||+--- value = • (x 20)
||+---- value = • • (x 21)
|+----- value = (x 22)
+------ value = • • • • • • • • (x 23)
---------------------------------------
Add up all the dots: eleven dots !!
Eleven expressed in decimal number = 11(10)
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The binary number system as
a representation system for
numerical values
illustrated
The binary number system is also a representation system for (unsigned) numerical values:
