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 |
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 !! |
The decimal number system is a representation system for (unsigned) numerical values:
The computer (due to electrical switch as memory cell) uses:
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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) |
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) |
The binary number system is also a representation system for (unsigned) numerical values: