Tue, Jun
3 New Articles

TechTip: Compacting a Large Number into a Small Space

  • Smaller Small Medium Big Bigger
  • Default Helvetica Segoe Georgia Times

Use Base 36 to squeeze the character representation of large numbers into a small space without using binary.

Almost every developer has run into this scenario. The boss announces you're integrating your legacy ERP software with an external system. You've been tasked to find a place to store a transaction ID from the external system in your legacy INVOICE table. Neither changing the existing table definition nor creating a new table is an option. Reviewing the INVOICE table, you rejoice to find an unused CHAR(6) user-defined field. This is where you'll store the transaction ID. Thereafter, your countenance falls when you find that the transaction ID requires eight digits. Everyone knows this is a lost cause because you can't cram eight digits into CHAR(6). Or can you?


One possible solution to this problem is converting the transaction ID to a binary integer format (such as an SQL BIGINT or RPG 20I 0) and slamming the result (truncating the first two bytes) into the CHAR(6) column. The only drawback to this solution is that the host application may cause a problem when displaying the binary data on the green-screen or when giving the data to a web site for display. Therefore keeping the number in text format is important.


Fortunately, there are other solutions that don't require binary conversion.


One such resolution would be to convert the eight-digit decimal number to hex. Whereas decimal is a base 10 numbering system (with 10 digits 0-9), hex is Base16 (with 10 digits and six letters, A-F). When storing a numeric value in a character column with hex, each position in the CHAR(6) column can hold 16 values instead of 10. Storing a decimal number in a CHAR(6) column will allow 1,000,000 (10^6) combinations from 0 through 999,999. Storing the number as hex will allow 16,777,216 combinations ranging from 0 through 16,777,215another six million values! The largest six-character number represented with hex is FFFFFF. Storing an integer as a hex value isn't as efficient as storing as binary, but it uses characters that are safe to display. Even though the largest possible number we can accept in hex is 16.7 million, perhaps this isn't big enough to hold the possible values received over the life of the application.


Another option, which offers yet more compaction, is to convert the numeric transaction ID value to Base 36 (also known as hexatridecimal or hexatrigesimal). Using the Base 36 numbering system allows each position in the CHAR(6) column to hold 36 values (with 10 digits and 26 English alphabet letters). In total, storing a number as Base 36 will allow a storage range of 0 through 2,176,782,335 (36^6). This method gives about half of the storage values of an unsigned 32-bit integer. Not a bad tradeoff. Even a CHAR(3) column can store 36^3 (46,656) values when using Base 36.


The table below shows various decimal numbers represented in hex and hexatridecimal.


Decimal   (Base10)

Hexadecimal   (Base 16)

Hexatridecimal   (Base 36)




















The attached RPG service program BASE36R contains two subprocedures (CvtToBase36 and CvtFromBase36) that convert between big integers and Base 36 and vice versa.


The RPG program should be accessible to users on V5R4 or higher (it can be modified for earlier versions). The logic to convert a number to Base 36 is basic; just continue to divide a number by 36 and assign the remainder as the appropriate character (0-9 or A-Z). The quotient is saved for the next iteration of the same logic until the quotient is zero. I used the PHP implementation shown on the Wikipedia page as the basis for the RPG code.


The reason for using characters A-Z is to make sure everything stored is readable in character-based storage; otherwise, we could just convert to binary. Base 36 is only one of many such systems that can be implemented.


Further, these conversion routines can be made available to DB2 for i-enabled applications by defining external user-defined function wrappers on the RPG code as shown here (IBM i 6.1 users and prior should remove "OR REPLACE" option):



(Number BIGINT)










(Base36Value VARCHAR(16) CCSID 37)









The function is easy to use. The following query returns the scalar result 1ZCX4D6M69:


SELECT Base36Value

FROM (VALUES(CvtToBase36(201311271224001))) X(Base36Value);

Uses for Base 36

I recently had a coworker use this technique. Our software is tasked with giving an export to a legacy system that can't be upgraded. The legacy system's job is to manipulate the data and send it back. A numeric transaction ID is slapped into a CHAR(6) column and remains untouched by the external system so that our software can keep track of each piece of information when it comes back. Once the transaction ID had reached one million, the link to the external system broke because the export file couldn't be changed to hold a CHAR(7) transaction ID.


The implemented fix was to convert our software's transaction ID to Base36 and continue to put it in the export file as CHAR(6). The legacy system could then process the file and send it back. Our software would read the Base 36 transaction ID, convert it back to numeric, and continue processing as usual. Using Base 36, we won't have to worry about the problem again until the transaction ID reaches 2 billion!


Other uses for Base 36 involve shrinking long numbers for readability. Say a serial number of 201311271224001 will be placed on a label that a user may need to read to a customer support rep someday. If this code is converted to Base 36, it's potentially easier to read: 1ZCX4D6M69. Further, the Base 36 representation can fit on a smaller label and provides the luxury of using a larger font. The Wikipedia entry on Base36 gives several more instances of how it's used in the industry.

A Few Notes

  • Do not confuse changing the representation of a number using Base 36 with Base64 encoding. The two are not related! Base64 is used to encode binary information using only 64 standard ASCII characters, so it actually makes the encoded data larger than the original.
  • Left-justified Base 36-encoded numbers do not sort, especially in EBCDIC! Convert the Base 36 to decimal/integer to sort correctly.
  • When dealing with negative numbers, the smallest number the RPG program can handle is -9223372036854775807 instead of the expected -9223372036854775808. This is because of how the program works with positive numbers when doing the calculations.


In summary, Base36 allows for the compacting of the character representation of numeric data without resorting to a binary conversion. Base36 can help with data exchange and readability issues to name a few uses.

Michael Sansoterra is a DBA for Broadway Systems in Grand Rapids, Michigan. He can be contacted at This email address is being protected from spambots. You need JavaScript enabled to view it..



Support MC Press Online

$0.00 Raised:

Book Reviews

Resource Center

  • SB Profound WC 5536 Have you been wondering about Node.js? Our free Node.js Webinar Series takes you from total beginner to creating a fully-functional IBM i Node.js business application. You can find Part 1 here. In Part 2 of our free Node.js Webinar Series, Brian May teaches you the different tooling options available for writing code, debugging, and using Git for version control. Brian will briefly discuss the different tools available, and demonstrate his preferred setup for Node development on IBM i or any platform. Attend this webinar to learn:

  • SB Profound WP 5539More than ever, there is a demand for IT to deliver innovation. Your IBM i has been an essential part of your business operations for years. However, your organization may struggle to maintain the current system and implement new projects. The thousands of customers we've worked with and surveyed state that expectations regarding the digital footprint and vision of the company are not aligned with the current IT environment.

  • SB HelpSystems ROBOT Generic IBM announced the E1080 servers using the latest Power10 processor in September 2021. The most powerful processor from IBM to date, Power10 is designed to handle the demands of doing business in today’s high-tech atmosphere, including running cloud applications, supporting big data, and managing AI workloads. But what does Power10 mean for your data center? In this recorded webinar, IBMers Dan Sundt and Dylan Boday join IBM Power Champion Tom Huntington for a discussion on why Power10 technology is the right strategic investment if you run IBM i, AIX, or Linux. In this action-packed hour, Tom will share trends from the IBM i and AIX user communities while Dan and Dylan dive into the tech specs for key hardware, including:

  • Magic MarkTRY the one package that solves all your document design and printing challenges on all your platforms. Produce bar code labels, electronic forms, ad hoc reports, and RFID tags – without programming! MarkMagic is the only document design and print solution that combines report writing, WYSIWYG label and forms design, and conditional printing in one integrated product. Make sure your data survives when catastrophe hits. Request your trial now!  Request Now.

  • SB HelpSystems ROBOT GenericForms of ransomware has been around for over 30 years, and with more and more organizations suffering attacks each year, it continues to endure. What has made ransomware such a durable threat and what is the best way to combat it? In order to prevent ransomware, organizations must first understand how it works.

  • SB HelpSystems ROBOT GenericIT security is a top priority for businesses around the world, but most IBM i pros don’t know where to begin—and most cybersecurity experts don’t know IBM i. In this session, Robin Tatam explores the business impact of lax IBM i security, the top vulnerabilities putting IBM i at risk, and the steps you can take to protect your organization. If you’re looking to avoid unexpected downtime or corrupted data, you don’t want to miss this session.

  • SB HelpSystems ROBOT GenericCan you trust all of your users all of the time? A typical end user receives 16 malicious emails each month, but only 17 percent of these phishing campaigns are reported to IT. Once an attack is underway, most organizations won’t discover the breach until six months later. A staggering amount of damage can occur in that time. Despite these risks, 93 percent of organizations are leaving their IBM i systems vulnerable to cybercrime. In this on-demand webinar, IBM i security experts Robin Tatam and Sandi Moore will reveal:

  • FORTRA Disaster protection is vital to every business. Yet, it often consists of patched together procedures that are prone to error. From automatic backups to data encryption to media management, Robot automates the routine (yet often complex) tasks of iSeries backup and recovery, saving you time and money and making the process safer and more reliable. Automate your backups with the Robot Backup and Recovery Solution. Key features include:

  • FORTRAManaging messages on your IBM i can be more than a full-time job if you have to do it manually. Messages need a response and resources must be monitored—often over multiple systems and across platforms. How can you be sure you won’t miss important system events? Automate your message center with the Robot Message Management Solution. Key features include:

  • FORTRAThe thought of printing, distributing, and storing iSeries reports manually may reduce you to tears. Paper and labor costs associated with report generation can spiral out of control. Mountains of paper threaten to swamp your files. Robot automates report bursting, distribution, bundling, and archiving, and offers secure, selective online report viewing. Manage your reports with the Robot Report Management Solution. Key features include:

  • FORTRAFor over 30 years, Robot has been a leader in systems management for IBM i. With batch job creation and scheduling at its core, the Robot Job Scheduling Solution reduces the opportunity for human error and helps you maintain service levels, automating even the biggest, most complex runbooks. Manage your job schedule with the Robot Job Scheduling Solution. Key features include:

  • LANSA Business users want new applications now. Market and regulatory pressures require faster application updates and delivery into production. Your IBM i developers may be approaching retirement, and you see no sure way to fill their positions with experienced developers. In addition, you may be caught between maintaining your existing applications and the uncertainty of moving to something new.

  • LANSAWhen it comes to creating your business applications, there are hundreds of coding platforms and programming languages to choose from. These options range from very complex traditional programming languages to Low-Code platforms where sometimes no traditional coding experience is needed. Download our whitepaper, The Power of Writing Code in a Low-Code Solution, and:

  • LANSASupply Chain is becoming increasingly complex and unpredictable. From raw materials for manufacturing to food supply chains, the journey from source to production to delivery to consumers is marred with inefficiencies, manual processes, shortages, recalls, counterfeits, and scandals. In this webinar, we discuss how:

  • The MC Resource Centers bring you the widest selection of white papers, trial software, and on-demand webcasts for you to choose from. >> Review the list of White Papers, Trial Software or On-Demand Webcast at the MC Press Resource Center. >> Add the items to yru Cart and complet he checkout process and submit

  • Profound Logic Have you been wondering about Node.js? Our free Node.js Webinar Series takes you from total beginner to creating a fully-functional IBM i Node.js business application.

  • SB Profound WC 5536Join us for this hour-long webcast that will explore:

  • Fortra IT managers hoping to find new IBM i talent are discovering that the pool of experienced RPG programmers and operators or administrators with intimate knowledge of the operating system and the applications that run on it is small. This begs the question: How will you manage the platform that supports such a big part of your business? This guide offers strategies and software suggestions to help you plan IT staffing and resources and smooth the transition after your AS/400 talent retires. Read on to learn: