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2000

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Document:	PDP7 appNote701
Order Number:	XX-D3317-50
Revision:
Pages:	4
Original Filename:	http://bitsavers.org/pdf/dec/pdp7/PDP7_appNote701.pdf

OCR Text

APPLICATION NOTE 701

PROGRAM
PDP-7 Gray Code Conversion
COMPUTER SYSTEM
PDP-7 with special lOT instructions that permit the input of an encoded number
in Gray binary.
DESCRIPTION
n
The Gray code is a specific n bit counting sequence of 2 counts having the
characteristics of being nonweighted, monostrophic (binary codes in which only one bit changes
from count to count) and reflected (represents a numbering system of a radix r, and by complementing a given bit, which is the same bit for all counts and is usually the most significant
bit, will yield the r-1 l s complement of the original count) and represents a specific ordered
n
numbering system of 2 counts.
METHOD
Adjacent bits in the Gray word are compared. When they are equal, the corresponding normal bit is set to O. When they are different, the corresponding normal bit is set
to 1.
EXAMPLE
Gray binary input = 10100
Compute normal binary by comparing bits
1

Gray

Normal

~/~/~/~/~

SPECIFICATIONS
Timing
1. Size-oriented subroutine:
21 jJsec + 12.25 x N jJsec + 8.75 jJsec
average time = 210 jJsec for 18-bit Gray code word
2. Speed-oriented subroutine:
7 jJsec + 7 x N jJsec + 3.5K jJsec
average time = 101 .5 jJsec for 18-bit Gray code word
where N is the number of Gray bits = 1
where K is the number of Gray bits = 0

PDP

_ 3RA.R"

Page 2
Storage Requirements

1. Size-oriented subroutine
14 locations

2. Speed-oriented subroutine
3 + 31 locations
where I is the number of bits in the Gray code word
USAGE
The size-oriented routine is entered with the Gray code to be converted in the
AC. The routine returns with the converted number (in normal binary) in the AC.

LAC

JMS

GRYBIN

where A is the Gray code to be converted.
The speed-oriented routine is open coding, to be used when the number of
Grey code bits to be converted is known.

Size-Oriented Conversion Routine Flow Chart

Page 3
LISTING
Size-Oriented Routine
/GRAY CODE TO NORMAL BINARY - SIZE ORIENTED

GRYBIN,

DAC TEMP
LAC (-11
DAC COUNT
LAC TEMP
Cll RAL
SPl
XOR (400000
RAl
ISZ COUNT
JMP .-4
RAl
JMP I GRYBIN

/INITIALIZE COUNTER FOR 12-BIT CONVERSION
/FIRST NORMAL BIT - FIRST GRAY BIT

/MOVE NORMAL BIT
/HAVE 12 BITS BEEN CONVERTED
/NO - CONTINUE; lOOP
/MOVE LAST NORMAL BIT
/RETURN

STORAGE MAP
TEMP
COUNT

(Gray number to be converted) C (TEMP)
Contains indexable constant for 12-bit conversion

SPEED-ORIENTED IN-liNE CODING
/MAIN PROGRAM
Cll RAl
SPl
XOR (400000
RAl
SPl
XDR (400000
RAl
/REPEAT UNTil I BITS HAVE
/BEEN CONVERTED
RAl
/MAIN PROGRAM
DEFINITION OF TERMS
AC
C(AC)
C(A) C(B)
lOT

Accumulator
Contents of AC
Contents of B are replaced by the contents of A
Input-output transfer commands

LIBR.u.R

Page 4
COMPARISON OF NUMBER SYSTEMS
Binary
Gray

Normal

Decimal

1
11
10
110
111
101
100
1100
1101
1111
1110
1010
1011
1001
1000
11000

1
10
11
100
101
110
111
1000
1001
1010
1011
1100
1101
1110
1111
10000

1
2
3
4
5
6

7
8

9
10
11
12
13
14
15
16

6 R t, R'l