# Lecture N -1- PHYS Microcontrollers

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4 Lecture N -4- PHYS 3330 decrementing a value stored in the memory and continuing doing so until that value reaches zero), or to perform a certain action if one or more conditions occurred (for instance the analog input exceeded a certain value). Certainly, it is impossible to teach good programming skills in this short lecture, but with the above you will be equipped with the most basic concepts to complete the microcontroller lab.

5 Lecture N -5- PHYS 3330 Appendix Hexadecimal and binary numbers The CPU is built on a large number of logic gates and the memory stores information in bits that are typically grouped into words (see above). So it seems tempting to express all numbers in form of individual bits, i.e. by a number system based on base 2. Such a counting system is called binary number system. However, for an 8-bit word one would have to write 8 ones or zeros; or for a 16 bit word, one would have to write 16 ones and zeros etc. It does not require much explanation that this scheme is not very practical for most situations, but it is still sometimes handy when interacting with specific peripherals (for example to turn on or off an LED that s connected to one of the digital I/O pins). It turns out that our trusty decimal system ( base 10, hence the name) is not very handy for programming, since it does not line-up with typical word boundaries. These boundaries are typically a multiple of four or eight bits. A not very scientific but non-theless extremely useful choice is base 16 called the hexadecimal system 6. Base 16 can represent 4 bits in one digit and therefore nicely lines up at half-byte and byte boundaries. Fig. 4 shows an example of the decimal numbers from 0 to 18 for binary and hexadecimal representation. Please note that the right digit represents the lower four bits and the left digit represents the upper four bits of the byte. There is no such correspondence in the decimal representation. DECIMAL BINARY HEXADECIMAL b 0x b 0x b 0x b 0x b 0x b 0x b 0x b 0x b 0x b 0x b 0x0A b 0x0B b 0x0C b 0x0D b 0x0E b 0x0F b 0x b 0x b 0x12 Fig. 4: A comparison of decimal, binary and hexadecimal systems. Hexadecimal numbers are sometimes also written as 00h, 01h, 02h 6 Base 8 (called octal system) can also be a useful but has not gained the same traction since most words are multiples of 8 bits.

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