Hand held electronic calculators were developed after mainframe electronic computers and there was a period when programmers and computer engineers had to use mechanical calculators to do their base 8 and base 16 calculations. A number of specialised calculators were developed for their use.
The early computers were used for large scale data processing but were unsuitable for small scale, ad hoc calculations . These were still performed using mental arithmetic, slide rules, mechanical calculators such as addiators and many other devices.
Pre-printed tables were widely used in industry and commerce. For example, if a bookkeeper needed to multiple a price by a quantity to prepare an invoice they could lookup the answer in a book of tables, such as the ‘Ready Reckoner’.
These tables were particularly useful in the pre-decimal UK, where pricing seventeen items at three pounds, fourteen shillings and nine pence each [base 12, base 20 and base 10] could challenge the mental arithmetic skills of most shopkeepers.
Engineers used slide rules for their calculations and businessmen added and subtracted with hand held mechanical calculators such as the addiator.
Computer Engineers
The first computer engineers needed to do hexadecimal and other calculations, and, in the period before electronic calculators, a number of specialised mechanical calculators were developed. Some of these are shown below.
IBM Field Engineers Hexadecimal Adder
This device does simple base 16 addition and subtraction. The dials can be turned turned using the stylus shown protruding from the bottom RH corner. This design of calculator dates back to Pascal’s Pascaline. A similar design was used for business calculators, such as the Addometer and the Lightening Mechanical Calculator.
Such calculators were used by IBM engineers maintaining the IBM 360 range of computers. The calculator was used to calculate program entry point and computer software failure for the operating system and application pograms. That is, when a computer program started at entry point of 1A4B and computer failed at memory location 2B36, the exact memory location failure could be calculated. It shows a 4 digit read out for a 4-byte word or memory location.
An IBM programmer named Carl J. Lombardi invented the hexadecimal adder. He had the wooden prototype unit that he had built in his home shop in the 1950s. He used this to demonstrate his design to people at IBM and the Sterling Plastics company, who were later given the contract to make the calculator.
Hexadaisy
The Hexadaisy is a 7 inch diameter plastic disk which can be used for a wide range of hexadecimal calculations and conversions.
Instructions are given for the following operations:
* Calculation of Offset for Relative Addressing
* Addition of Hexadecimal Numbers
* Subtraction of Hexadecimal Numbers
* Two’s Complement of Hexadecimal Numbers
* Decimal to/from Hex Conversions
* Hex to/from Decimal Conversions
This is a specialised version of a circular slide rule.
Hex Adder
The Hex Adder was made by the Hexco company of Houston Texas. The company was started in 1967 by Tom and Linda Tarrant, both of whom had been Systems Engineers for IBM. Hexco began offering products for main-frame computer programmers. The first product was a hand-held manual calculator that added and subtracted in hexadecimal, the numbering system used in computers, hence the name, Hexco, for “hexadecimal company.” When I contacted the company they told me that they had long since ceased to make the Hex Adder, but had been contacted by the Smithsonian Museum in Washington and asked to take their tools out of store to make one final Hex Adder for the museum’s collection.
Hexadat and Octadat
The Addiator company made two hand held mechanical calculators for programmers and computer engineers. The Hexadat was for base 16 arithmetic and the Octadat for base 8 arithmetic.
In 1972 Hewlett-Packard introduced the HP-35, the first powerful and affordable [$395] electronic pocket calculator, and the mechanical calculators began to slip into history. Later, Texas Instruments introduced its Programmer hand-held electronic calculator which was able to operate in the decimal, octal, and hexadecimal number systems. It could also perform logical operations and to convert a number between the different number systems.
Calculating 
I worked with Carl Lombardi for about 6 years from 1970 to ’76 at IBM in Raleigh, NC. His office was right next to mine. He kept the wooden prototype for the calculator in his office. He had made it in the late 1960s, not the ’50s. IBM did start using hex until the 360 era in t bye mid 60s. I had one of these calculators myself that I had been issued only a year or so before I knew Carl. I wish I could find it now.