Representation Of Numbers; Normalization; Instruction Formats - RCA 70/46 Reference Manual

REPRESENTATION
OF NUMBERS
NORMALIZATION
INSTRUCTION
FORMATS
RX Format
Description
Floating-Point Instructions
• The mantissa is always represented in hexadecimal. An assumed radix
point is always immediately to the left of the high-order digit of the
mantissa.
The exponent, bits 1 through 7, indicates the power to which the number
16 must be raised. The range of the exponent is from -64 to +63 corre-
sponding to the binary value of 0-127. The power is equal to the binary
number minus 64, as shown in following table:
Exponent Decimal Equivalent
Power
(1 111 111) 2
127 -64
=
+63
(1 000 111)2 71 -64
=
+7
(0 000 000)2
o
-64
=
-64
Because the value (64)
10
represents the power zero, this technique is
called excess 64 notation.
The sign of a result from addition, subtraction, multiplication, or divi-
sion with a zero mantissa is positive. A zero sign, zero exponent, and zero
mantissa in a floating-point number is called true zero.
• A floating-point number with a mantissa containing a non-zero, high-
order, hexadecimal digit is called a normalized number. An unnormalized
number has one or more high-order hexadecimal zero digits in the mantissa.
To change an unnormalized number into a normalized number, the man-
tissa is shifted to the left until the high-order digit is non-zero. Then, the
exponent is decremented by the number of digits shifted.
Generally, normalization occurs when the intermediate arithmetic result
is changed to the final result. However, in multiplication and division
operations, normalization occurs before the arithmetic process.
Floating-point operations are performed with, or without, normaliza-
tion. Most operations are performed in only one way; however, addition
and subtraction may be performed either way as specified.
When normalization is not performed, high-order zeros in the result
mantissa are not eliminated. Depending on the original operands, the result
may, or may not, be normalized.
Initial operands in both normalized and unnormalized operations need
not be in normalized form. Because nornlalization takes place on hexa-
decimal digits, the three high-order bits of a normalized mantissa can
be zero.
• The following two instruction formats are used for floating-point
operations:
o
7 8 11 12 15 16 19 20 31
• An address is formed by adding the contents of general registers X2
and B2 to the displacement field D 2 . This address specifies a main memory
location that contains the second operand in the operation. Rl designates
the floating-point register containing the first operand.
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