1. IDENTIFICATION
1.1 Digital-8-14-U-Sym
1.2
Binary to Binary Coded Decimal Conversion
1.3
March 10, 1965
PDP-B
LIBRARY
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Binary to Binary Coded Decimal Conversion Subroutine for PDP-8, Study Guides, Projects, Research of Number Theory
A subroutine for converting binary data to binary-coded-decimal (BCD) format for typeout, magnetic tape recording, etc. The subroutine uses 33 storage locations and requires a standard PDP-8. It is called by the JMS instruction and returns the BCD result in the accumulator.
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1. IDENTIFICATION
1.1 Digital-8-14-U-Sym
1.2 Binary to Binary Coded Decimal Conversion
1.3 March 10, 1965
PDP-B
LIBRARY
Digital-8-14-U-Sym Page 3
After eight pases through the basic loop, the developed BCD representation is shifted left four bits and the "residual" least significant digit is added before exit.
6.2 Example
As an example consider the conversion of the binary equivalent of 512 decimal: 00 1 000 000 000 Successive calculations to obtain the most significant BCD digit are as follows: Link
a
a
Addition 00 1 000 000 000
11 a a 11 100 000
111 all 100 000
111 00 1 11 a 000
000 00 1 11 a 000
000 001 11 a 000
111 110 all 100
Notice that the remainder is the binary representation of 12 decimal. Writing
the I ink bits in the order they are developed gives 0101 the BCD character denoting 5.
6.3 Scaling
The original binary number must be no larger than 999 (decimal) which is equiva- lent to 1747 (octal). The binary point is assumed to be at the extreme right end of the word (to the right of bit position 11) and the decimal point is also so positioned.
and 11. 1 •
In other words, this subroutine converts binary integers to BCD integers. Note that the subroutine is designed for positive input only!
METHOD
Algorithm The algorithm is straightforward and is fully described in sections 6.1, 10.4,
EXECUTION TIME
Minimum
Digital-8-14-U-Sym
Page 4
Minimum execution time will occur when the number to be converted is from 0
to 9 inclusively. In this case, the execution time will be precisely 216.0 microseconds.
9.2 Maximum
Max imum execution time wi II occur when the number to be converted happens to
be 7.7X (decimal where X may represent any decimal digit). This time is precisely 235.
microseconds.
9.4 Tim ing Equation
Execution time for a particular BCD result may be calculated from the following
formula,
TIME = 216.0 + N x 3.
where N represents the number of bits of the two most significant BCD digits that are equal to
one.
For example, the binary equivalent of the decimal number 512 (010 100 010 010)
will take exactly
216.0 + 3X3.2 = 225.6 microseconds
to convert.
10. PROGRAM
10.4 Program Listing
A Iisting of the program with BCD located in 0200 appears as follows:
IBINARY TO BCD CONVERSION 3/6/65-DEC
IENTER WITH BINARY NUMBER «999(10))
liN ACCUMULATOR; EXIT WITH THREE CHARACTER
IBCD NUMBER IN ACCUMULATOR
lAC 0-3; AC 4-7; AC 8-11 WILL CONTAIN
ITHE BCD CHARACTERS Oi.l EXIT
IWEIGHTING: AC 0-3 100
I AC4-7 10 I AC 8-11 1
ISTORAGE 33(10) REGISTERS
11. DIAGRAM
11. 1 Flow Chart
POINTER
(L)·O
CLA TAD NUMBER RAL ISZ POINTER
SNL
ENTER
DATA -+ INPUT (CDNTROLl-+ POINTER CLL (COUNTl-+AC
(AC) _NUMBER TAD INPUT TAD TABLE
(L )'
(AC)_INPUT
CLL RTL CLL RTL TAD INPUT JMP I BCD
RETURN
Digital-8-14-U-Sym Page 6