CPSC 110, Spring 2002
with Brent M. Dingle
Knowledge Tidbit:
The computer stores “everything” as zeros or ones.
Why?
The
computer stores “everything” in its memory.
The computer’s memory is
composed of bytes (one kilobyte (kb or just k) is 1024 bytes)
Every byte contains 8 bits.
Every bit contains a zero or
a one.
This means numbers must be stored in BINARY form
(i.e. base 2).
Recall our “normal” numbering system is base 10.
In our normal numbering system the rightmost digit
represents how many ONEs there are.
The second rightmost digit represents how many TENs
there are.
The third rightmost digit represents how many
HUNDREDs there are,
The fourth rightmost digit represents how many
THOUSANDs there are and so on.
Notice that 100 = 1, 101 = 10,
102 = 100, 103 = 1000… pretty neat isn’t it?
For example:
1234 = ( 1 * 103 ) + (
2 * 102 ) + ( 3 * 101
) + ( 4 * 100 )
= ( 1 * 1000 ) + ( 2 * 100 ) + ( 3 * 10 )
+ ( 4 * 1 )
= 1000 + 200
+ 30 + 4
=
1234
Notice we use TEN symbols for digits ŕ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Binary (base 2) numbering works in the same fashion.
The rightmost digit represents how many ONEs there
are.
The second rightmost digit represents how many TWOs
there are.
The third rightmost digit represents how many FOURs
there are.
The fourth rightmost digit represents how many
EIGHTs there are, and so on.
For example:
0001 = ( 0 * 23
) +
( 0 * 22 ) + ( 0 * 21 ) + ( 1 * 20 )
= 0 + 0 + 0 + 1 =
1
0010 = ( 0 * 23
) +
( 0 * 22 ) + ( 1 * 21 ) + ( 0 * 20 )
= 0 + 0 + 2 + 0 =
2
0011 = ( 0 * 23
) +
( 0 * 22 ) + ( 1 * 21 ) + ( 1 * 20 )
= 0 + 0 + 2 + 1 =
3
0100 = ( 0 * 23
) +
( 1 * 22 ) + ( 0 * 21 ) + ( 0 * 20 )
= 0 + 4 + 0 + 0 =
4
0101 = ( 0 * 23
) +
( 1 * 22 ) + ( 0 * 21 ) + ( 1 * 20 )
= 0 + 4 + 0 + 1 =
5
:
1000 = ( 1 * 23
) +
( 0 * 22 ) + ( 0 * 21 ) + ( 0 * 20 )
= 8 + 0 + 0 + 0 =
8
:
1111 = ( 1 * 23
) +
( 1 * 22 ) + ( 1 * 21 ) + ( 1 * 20 )
= 8 + 4 + 2 + 1 =
15
Notice we use only TWO symbols for the digits ŕ 0, 1