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0000
00
0001
01
0010
02
Binary Position
8
4
2
1
0011
03
0100
04
Binary Value
0
1
0
1
010
1
05
y
Decimal Equivalent
=
05
06
01 11
07
1000
08
1001
09
1010
10
1011
11
1100
12
1101
13
1110
1
J1J
Figure 2-36.
Four-Digit Addressing
Six-DigiS Addressing
•
Six binary digits form 64 different
storage addresses.
•
~ddress
range from 000000 to 111111
(00-63 decimal).
If the original four binary digits pro-
vide 16 combination of numbers (2
4
=16),
then six binary digits can be used to
provide 64 combinations of numbers
(2 e =64).
By using these 6.4 numbers as
storage addresses, it is possible to
have 64 addressable storage locations
with the address range of 000000 to
111111 (00 - 63 decimal) •
There are several ways to apply the
six binary digits to an addressing
scheme.
For the purpose of this discus-
sion, it is most convenient to expand
the original 4-digit addressing scheme
shown in Figure 2-36.
Thus, in Figure
2-37, the four low-order binary digits
describe some number in the range
0000-1111 (00 to 15 decimal), while the
two high-order binary digits describe
which of the four groups of 16 numbers
is to be used.
In the example shown,
the four .low-order digits 1111 (15
decimal) combine with the two high-order
digits 10 (32 decimal) to select storage
loca tion 101111 (47 decimal).
Ten-Digit Addressing
•
Ten binary digits form 1,024 differ-
ent storage addresses.
•
14
15
Address range from 0000000000 to
1111111111 (0000-1023 decimal).
If four additional binary digits are
added to the 6 digit addressing scheme,
it is possible to define
1,024
storage
locations
(2~o=l,024).
To accommodate
the extra bits in the addressing scheme,
it is necessary to add another dimension
(Figure 2-38).
The four low-order binary digits
describe some basic number from 0000 to
1111.
This basic number is represented
by a storage location in each of the 64
blocks of 16 storage locations.
To
further select the desired location, the
next two binary digits describe one of
four blocks of 256 storage locations.
Each of these blocks is made up of 16
blocks of 16 storage locations each.
The six low-order digits have narrowed
the selection to 16 storage locations.
With four high-order digits, it is pos-
sible to make a final selection of one
of these 16.
In the example shown, the
four low-order digits 0000 (00 decimal) ,
plus the next two digits 01 (16
decimal), plus the four high-order
digits 1110 (896 decimal), combine to
form 1110010000 (912 decimal).
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