# Hexadecimal Numbering System - RCA Spectra 70 Training Manual

System
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OP
M
147
(16)
F(16)
0001(2)
4000(10)
When an instruction is staticized the displacement
is added to the base address. The absolute sum of
the two is called the effective address, and is the
address value actually used in execution.
In the
example above,
the displacement,
is added to the base address in
register 1,
resulting in an effective address
of
4000(10)
40000(10)
44000(10)
This technique makes it unnecessary to carry lengthy
addresses within instructions. Each displacement
is a fixed length of 12 bits. However, since the 16
least significant bits of general registers may be used
for base address values, it is possible to access
locations which require 13, 14, 15,
or 16 bit
addresses.
This addressing concept is a necessary feature in
larger members of the Spectra 70 series where ad-
dresses may exceed 16-bit lengths.
The maximum value of a displacement is 4095(10)'
r - , - -
2,048 1.024 512 256 128
211
2 10
2
9
2 8
27
r----
1
1
1
1
1
.
--
64 32 16
8
4
2
2 6 2 5 24 2 3 22 21
1
1
1
1
1
1
1 DECIMAL VALUE
-~
2° POWER OF TWO
1
BINARY ADDRESS
2
4
8
16
32
64
128
256
512
1024
2048
4095
When addressing locations between 0000(10) and
4095(10)' no base address need be associated with
a displacement. The 12-bit address carried in the
D1 or D2 fields becomes a direct address when the
value 0000(2) is placed in the corresponding B1 and
B2 fields.
HEXADECIMAL NUMBERING SYSTEM
The binary system, although efficient for the 70/25,
is not a convenient notation for the programmer. The
hexadecimal numbering system, which operates on
the base sixteen, is a convenient method to express
the binary representation of HSM addresses.
The decimal system is a numbering system based
upon the number ten. It uses ten single symbols
(0-9) to represent the basic digits. By a system of
positional notation that indicates multiplication by
4
powers of the base, any value can be expressed. The
hexadecimal system requires sixteen symbols to ex-
press its basic digits. The alphabetic letters A
through
F
have been assigned to represent the decimal
values 10 through 15 in order to maintain single
symbols for the digital values of the hexadecimal
system.
Each symbol in the hexadecimal system can be
expressed by four bits in the binary system. There-
fore, two hexadecimal marks are required to repre-
sent a byte, and four hexadecimal marks can express
an HSM address.
HEXADECIMAL
BINARY
DECIMAL
0
0000
0
1
0001
1
2
0010
2
3
0011
3
4
0100
4
5
0101
5
6
0110
6
7
0111
7
8
1000
8
9
1001
9
A
1010
10
B
1011
11
C
1100
12
D
1101
I
13
E
1110
I
14
F
1111
I
15
Conversion of Hexadecimal to Decimal
The decimal number 472 represents:
4 x 100 + 7 x 10 + 2 x 1
=
(472)10
The binary number (101101)2 can be converted
to its decimal equivalence by:
1 x 2 5 + 0 x 24 + 1 x 2 3 + 1 x 22 + 0 x 21
32
+
0
+
8
+
4
+
0
+
1
x
2 0
+
1
=
(45)10
A hexadecimal number is converted to a decimal
value by multiplying the hexadecimal characters
by the appropriate value of 1 G n .

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Spectra 70/25