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DIGITAL-8-10-U

December 1965

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Document:	digital-8-10-u-d
Order Number:	DIGITAL-8-10-U
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IDENTIFICATION
I .I

Digital-B-IO—U-Sym

I .2

Binary-Coded—Decimal to Binary Conversion Subroutine

I .3

March I, I965

POP-8
LIBRARY

Dig ital-8- l O-U-Sym
Page 2
2.

ABSTRACT
A basic subroutine for converting binary-coded-decimal numbers to their

equivalent binary value.

Conversion is accomplished by "radix deflation.

REQUIREMENTS

3. l

Storage

This subroutine requires 23 (decimal) memory locations.
3.3

Equipment
Standard PDP-8.

USAGE

4.l

Loading
Load the subroutine with the Binary or RIM Loader.

4.2

Calling Sequence
Call with the number to be converted in the AC.

Return will be to the location

following the calling JMS with the result in the AC.
6.

DESCRIPTION

6 .1

Discussion

The method used is thatof "radix deflation.

”

Upon entry, the BCD number may

be considered to be in the following form.

D2162+D116+D°

6.1.1.E

What is desired is the number in the form.

D2l02+D110+D°

6.].2.E

The PDP-8 can shift (rotate) and add.

A right shift is equivalent to a division by a power of

An appropriate series of shifts, additions, and subtractions is used to convert the number
from the form of 6.l l .E to that of 6. l .2.E.

two.

6.2

Example
Consider the BCD number

Digital-8-10—U-Sym
Page 3
0101

0001

1001

representing the decimal number 519.
First, the whole number is stored and then brought back into the AC. Next, the
four most significant bits are masked out. At this point, the accumulator contains 16x16xA or
0101

0000

1000

0000

A shift to the right of one bit yields

0010

This number is stored and then brought back to the AC, shifted right two bits, and the stored
value added as follows
0000

1010

0000

0010

1000

0000

0011

0010

0000

Now the original number is added to this result
0011

0010

0000

0101

0001

1001

1000

0011

1001

and the most significant eight bits masked out as

1000

This is stored,

0011

0000

brought back and shifted right once,and the stored value added.
0100

0001

1000

0011

0000

1100

0100

1000

Next the result of this addition is shifted right two places dividing the number by four as follows
0011

0001

0010

negated and the original number added
1100

1110

0101

0001

1001

0010

0000

0111

This result represents in binary 512 plus 4 plus 2 plus 1
6.3

519,the original number.

Scaling
This subroutine assumes an integral BCD number and yields an integral binary

equivalent.

Digital-8— I O-U-Sym
Page 4
METHOD

7.2

Algorithm
The algorithm used is illustrated step by step in Section 10.4.

EXECUTION TIME
9.2

Maximum
The maximum

(and invariant) execution time of this subroutine is 49.6 microseconds.

10.

PROGRAM

10.4

Program Listing
A listing of the subroutine with BCDBIN located at 0200 is given below.

simplify mnemonics D

and

0200

0000

0201

3223

DCA TEMPPP

0202

1223

0203

0225

TAD TEMPPP
AND MASKKA

0204

7110

CLL RAR

0205

3224

DCA TEMPPQ

BCDBIN,

0206

1224

TAD TEMPPQ

0207

7012

RTR

0210

1224

TAD TEMPPQ

0211

1223

TAD TEMPPP

0212

0226

AND MASKKB

0213

3224

DCA TEMPPQ

0214

I224

TAD TEMPPQ

0215

7110

CLL RAR

0216

1224

TAD TEMPPQ

0217

7012

RTR

0220

7041

CIA

0221

1223

TAD TEMPPP

/ABC IN BCD CODE IN AC
/16 (16A + B) + c
/16 (16A)
/8 (16A)

/8 (16A)
/2 (16A)
/10 (16A)
/16 (26A + B) + C
/16 (26A + B)
/16 (26A + B)
/8 (26A + B)
/24 (26A + B)
/6 (26A + B)
/—6 (26A + B)
/16 (16A + B) + C -6 (26A+ B)
/=16x16A 6x26A + 16B 6xB+C
/= 100A +1013 + c
/BINARY VALUE IN AC
-

0222

5600

JMP I BCDBIN

0223

0000

0224

0000

0225

7400

0226

7760

TEMPPP;
TEMPPQ,
MASKKA,
MASKKB,

have been replaced respectively with A, B, and C.

—

7400
7760

/MASK FOR MOST SIG. FOUR BITS
/MASK FOR MOST SIG. EIGHT BITS

Digital-8— l O-U—Sym
Page 5
12.

REFERENCES

12.3

DECUS Programs
See DECUSCOPE January l965, article entitled ”Accelerated Radix Deflation

l4.

the PDP—7 and PDP-8."

ACKNOWLEDGEMENTS

Mr. Donald V. Weaver, Consultant, of New York City, who first described the
algorithm used by this subroutine in reference l2.3 has granted his kind permission to include

this subroutine in the PDP-8 library so that a detailed description may be available.