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].

The Hexadat, Octadat and Hex Adder mechanical calculators. The Hexadat and Hex Adder add and subtract to base 16.

A single sheet of instructions was provided with the Octadat.

Back of calculator with label giving name of importer

In mathematical numeral systems, the radix or base is the number of unique digits, including zero, that a positional numeral system uses to represent numbers.

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