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cally is a group of symbols.
Each sym-
bol in a number has a definite place and
value.
The place value of the digit symbol is
some power of the base.
The power of
the base starts with zero and increases
by one from right to left.
The base of
the decimal numbering system in common
usage is ten (10).
Example:
444
=
4x10
a
+4x10'+4x10
0
(10
0
= 1)
/ l"
Digit Base Place
444 = 400+40+4
The maximum value of a symbol is
always one less than the base.
In our
above example. the base is ten (10) so
the maximum value is nine
(9).
If when
adding two symbols the total exceeds the
base. a carry (value of one) is added to
the next higher place.
Example:
6
+6
Carry
12
BASIC BINARY
Units of Binary
This is a numbering system using a base
of two.
All of the rules which we dis-
cussed for a numbering system apply
here.
Let us check.
The base is two so the maximum symbol
value is one.
The binary numbering
system has only two valid symbols, 0 and
1.
Example:
Digit
Base
Place
" ' \ /
0101 = Ox2 3+ 1x2
:a.O
x 2'+1x2
0
decimal
5
o
o
1
1-22
Binary-Decimal Conversion
The decimal place values of a six posi-
tion binary number are:
32
16
8
4
2
1
1x2
0
1
1
1
1
1
The preceding binary number equals
63
when the place values are added.
The following chart shows conversion
from decimal to binary:
Decimal
Binar:l
0
0000
1
0001
2
0010
3
0011
4
0100
5
0101
6
0110
7
0111
8
1000
9
1001
10
1010
11
1011
12
1100
13
1101
14
1110
15
1111
ZONED DECIMAL - EXTENDED BINARY CODED
DECIMAL (BCD)
Zoned decimal is a decimal number rep-
resenting a BCD alphanumeric character.
A zoned decimal has eight places divided
into two II-place sections.
The high-
order places represent the alphanumeric
zone bit and the low-order places
represent the alphanumeric decimal.
Example: 1101
011,=P
11
7
(zone) (digit)
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