Abstract
Microcontrollers represent a major means of digital processing As such, a basic appreciation of digital concepts is necessary as a foundation to understanding both their software and hardware fields of operation.
Starting with the digital pattern data representations; the binary arithmetic operations of addition, 2’s complement subtraction, multiplication and division together with Boolean algebra and logic gates are developed with sufficient rigor to support the material presented in following chapters.
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Notes
- 1.
Of course, there are lots of digital encoding standards; for instance, the 6-dot Braille code for the visually impaired.
- 2.
As did Babbage’s mechanical computer of a century earlier.
- 3.
And ten toes, but base-20 systems are rare though not unknown.
- 4.
The binary base is not a new fangled idea invented for digital computers; some cultures have used base 2 numeration in the past. The Harappān civilization existed more than 4000 years ago in the Indus River basin. Found in the ruins of the Harappān city of Mohenjo-Daro, in the beadmakers’ quarter, was a set of stone pebble weights. These were in ratios that doubled in the pattern, 1,1,2,4,8,16,…, with the base weight of around 25 g (≈1 oz). Thus bead weights were expressed by digits which represented powers of 2; that is, in binary.
- 5.
Microprocessors and microcontrollers are closely related (see Fig. 3.8 on p. 59) and so we will often use the terms interchangeably.
- 6.
The b’⋅⋅⋅’ notation is not universal; for example, (1111011110) 2 is an alternative. If the base is unambiguous then the base indicator may be omitted.
- 7.
Other representations for the hexadecimal base are 8C140A h and 0x8C140A.
- 8.
Many scientific calculators, including that in the Accessories group under Microsoft’s Windows, can do hexadecimal (and binary) arithmetic.
- 9.
Sometimes called 8-4-2-1 code after the weightings of the first four lowest columns.
- 10.
Which you had to do way back in the mists of time in primary/elementary school!
- 11.
If you enter a negative decimal number in the Microsoft Windows calculator and change base to Binary, the number will be displayed in 2’s complement form.
- 12.
The first professor of mathematics at Queen’s College, Cork.
- 13.
A true story from Dr. Seamus Laverty. In days of yore when logic circuits were built out of discrete devices, such as diodes, resistors and transistors, problems arising from sneak current paths were rife. In one such laboratory experiment the output lamp was rather dim, and the lecturer in charge suggested that two NOTs in series in a suspect line would not disturb the logic but would block off the unwanted current leak. On returning sometime later, the students complained that the remedy had no effect. On investigation the lecturer discovered two knots in the offending wire—obviously not tied tightly enough!
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Katzen, S. (2010). Digital Representation. In: The Essential PIC18® Microcontroller. Computer Communications and Networks. Springer, London. https://doi.org/10.1007/978-1-84996-229-2_1
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