# Category Archives: Computing Calculators

## The Octadat base 8 mechanical calculator for computer programmers

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  base 8 and base 16 calculations. A number of specialised calculators were developed for their use.

Octal and hex are convenient ways to represent binary numbers. Computer engineers often need to write out binary quantities, but in practice writing out a binary number, such as 1001001101010001, is tedious and prone to errors. Therefore, binary quantities are written in a base-8, or “octal”, or,  more commonly, a base-16, “hexadecimal” or “hex”, number format.

In the decimal system, there are 10 digits, 0 through 9, which combine to form numbers. In an octal system, there are only 8 digits, 0 through 7. That is, the value of an octal “10” is the same as a decimal “8”, an octal “20” is a decimal “16”, and so on.

Octal became widely used in computing when systems such as the PDP-8, ICL 1900 and IBM mainframes employed 12-bit, 24-bit or 36-bit words. Octal was an ideal abbreviation of binary for these machines because their word size is divisible by three (each octal digit represents three binary digits). So four, eight or twelve digits could concisely display an entire machine word. It also cut costs by allowing Nixie tubes, seven-segment displays, and calculators to be used for the operator consoles, where binary displays were too complex to use, decimal displays needed complex hardware to convert radices, and hexadecimal displays needed to display more numerals.

Calculator, stylus and leather case

The Octadat mechanical calculator was made by Addiator Gesellschaft of Germany and was used for base 8 addition and subtraction. It has been reported that it was manufactured between 1968 and 1970 and about 3,000 units were produced.   The calculator is 160mm x 37mm.

The company also made a base 16 calculator called the Hexadat [see this post]. Some American companies also made base 16 mechanical calculators [see this post].

Filed under Calculators, Computing Calculators

## The Hexadat base 16 mechanical calculator for computer programmers

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 Hexadat is a base 16 mechanical pocket calculator that was made for computer engineers and programmers.

The Hexadat  calculator was made by Addiator Gesellschaft of Germany and was used for base 16 addition and subtraction. Base 16 [hexadecimal or  hex] is a positional numeral system. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, and A, B, C, D, E, F  to represent values ten to fifteen. For example, the hexadecimal number 2AF3 is equal, in decimal, to (2 × 163) + (10 × 162) + (15 × 161) + (3 × 160), or 10,995. Addiator patented the Hexadat on the 24th January 1967. It was manufactured from 1967 to some time in the early 1970s.

Other base 16 mechanical calculators in use at the time were the IBM Field Engineers Hexadecimal Adder, the Hex Adder and the Hexadaisy [see this post]. They were used during the period  between the development of the electronic computer and the development of an electronic pocket calculator capable of hexadecimal arithmetic.  Addiator Gesellschaft also made a base 8 calculator called the Octodat [see this post].

A complete unit is shown in the photographs below. The Hexadat is larger than most other addiators at 61 x 232 x 4 mm [2.4 x 9.1 x 0.2 inches]. The stylus has a ball point pen at its  other end and is held in a loop in the zipped case. A label on the back of the Hexadat indicates that it was sold by Data Efficiency Limited of Hemel Hempstead, England.

The instruction sheet is dated October 1967.

The marks on the paperwork are artefacts of scanning.

Side 1

Side 2

Manufacturers literature

The Addiator factory in Wolfach, Germany

In August 1977 Texas Instruments started selling the TI Programmer electronic pocket calculator. This performed the four basic arithmetical operations in decimal, hexadecimal and octal. It could also convert between base 10, base 16 and base 8. It cost \$42.50 and killed the market for the Hexadat.

Filed under Calculators, Computing Calculators

## Mechanical Calculators for Computer Engineers

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.

1 Comment

Filed under Calculators, Computing Calculators