Compressing Data into a Few Bits

Suppose we gave some data consisting of:

a room number (3 digits)
the combination to a safe (three 2-digit numbers each 00 to 59)
a 2-digit number indicating what department uses this room (1 to 12)

We would like to store this information in as little space as we can. How can we do that?

We can store the Room Number in 10 bits.
We can store each number in the combination as 6 bits.
We can store the Department number in 4 bits.

That will add up to 32 bits or 4 bytes.

What would the code look like? Suppose we have:

CARD     DS  0C
ROOM     DS  ZL3   (Room number)
         DS  CL2
C1       DS  ZL2   (Combination number 1)
         DS  CL2
C2       DS  ZL2   (Combination number 2)
         DS  CL2
C3       DS  ZL2   (Combination number 3)
         DS  CL2
DEPT     DS  ZL3   (Department number)
         DS  60C

We will store the values in this fashion:

       ROOM   C1     C2     C3     DEPT

bits   0-9   10-15  16-21  22-27   28-31

To achieve this, we need to use PACK, CVB, shifts and AR. Suppose we have:

         XREAD CARD,80
*           
         PACK   TEMP(8),ROOM(3)   Pack the ROOM value
         CVB    5,TEMP            Convert it to binary 
         SLL    5,22              Move it over to bits 0-9 
*
         PACK   TEMP(8),C1(2)     Pack the C1 value
         CVB    6,TEMP            Convert it to binary       
         SLL    6,16              Move it over to bits 10-15  
*
         PACK   TEMP(8),C2(2)     Pack the C2 value
         CVB    7,TEMP            Convert it to binary
         SLL    7,10              Move it over to bits 16-21 
*
         PACK   TEMP(8),C3(2)     Pack the C3 value
         CVB    8,TEMP            Convert it to binary   
         SLL    8,4               Move it over to bits 22-27 
*
         PACK   TEMP(8),DEPT(2)   Pack the DEPT value
         CVB    9,TEMP            Convert it to binary
*                                 Is is already in bits 28-31
*
         AR     5,6               Combine the values 
         AR     5,7               in the five registers   
         AR     5,8
         AR     5,9
*

At the end of this, register 5 contains the 32 bits we want. We can use STCM or L to put the data in a variable somewhere.

Invent some data and try working through this by hand.

Suppose we have used STCM to put the 4-byte value somewhere in a table in a field called OFFICE.

We now might want to extract and print all this data. Ultimately we will print the values by having them in packed decimal variables and then using ED, but what do we do first?

Suppose we have:

ROOMP    DS   PL2
C1P      DS   PL2
C2P      DS   PL2
C3P      DS   PL2
DEPTP    DS   PL2

How do we extract the data from OFFICE into these variables?

         ICM  5,B'1111',OFFICE    Get the value in a register
         SLL  5,28                Arrange to have 0s everywhere
         SRL  5,28                except bits 28-31
         CVD  5,TEMP              Convert it to packed decimal 
         ZAP  DEPTP(2),TEMP+6(2)  Copy the value into DEPTP
*
         ICM  5,B'1111',OFFICE    Get the value in a register
         SLL  5,22                Arrange to have 0s everywhere 
         SRL  5,26                except bits 22-27 and then
*                                 move them to bits 26-31
         CVD  5,TEMP              Convert it to packed decimal
         ZAP  C3P(2),TEMP+6(2)    Copy the value into C3P
*
         ICM  5,B'1111',OFFICE    Get the value in a register
         SLL  5,22                Arrange to have 0s everywhere 
         SRL  5,26                except bits 16-21 and then
*                                 move them to bits 26-31
         CVD  5,TEMP              Convert it to packed decimal
         ZAP  C2P(2),TEMP+6(2)    Copy the value into C2P
*
         ICM  5,B'1111',OFFICE    Get the value in a register
         SLL  5,22                Arrange to have 0s everywhere 
         SRL  5,26                except bits 10-15 and then
*                                 move them to bits 26-31
         CVD  5,TEMP              Convert it to packed decimal
         ZAP  C1P(2),TEMP+6(2)    Copy the value into C1P
*
         ICM  5,B'1111',OFFICE    Get the value in a register
         SLL  5,22                Arrange to have 0s everywhere 
         SRL  5,26                except bits 0-9 and then
*                                 move them to bits 22-31
         CVD  5,TEMP              Convert it to packed decimal
         ZAP  ROOMP(2),TEMP+6(2)  Copy the value into ROOMP

TEMP DS D

Again: invent some data and try working through this by hand.