Electronics Technology | |
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Binary Math
When considering how electronic machines are able to perform mathematical computations, it is important to realize that the machine is likely using an ALU, arithmetic logic unit. The simplest of these are programmable adders which are able to switch between adding and logic functions. When adding, there are two binary bits, known as flags, which help keep track of the results. One is the carry flag or C flag which indicates that the results of an addition produced an answer that could not fit in the results register. The other is the zero flag or Z flag, which indicates that the results of an addition or logic function was zero.
Subtraction is done by adding a negative number. In binary, negative numbers are represented using the 2’s complement method. The two’s complement is performed by taking the 1’s complement and then adding one. The 1s complement is simply the invert of each and every bit in a register. For example, the 8 bit binary equivalent of 27 decimal is 00011011 in binary. The one’s complement of 00011011 is 11100100. If we add one to this, we get 11100101 which is interpreted as -27.
To help with these concepts, I have developed tools which you can experiment with, The first is the 8 bit number line, and the second is the 2’s complement calculator. Try them out. See if you can familiarize yourself with these concepts by making up some problems and predict the answers.
Digital Electronics:
For those starting out in digital electronics, The first concept that you will need to understand is gates. There are two basic gates AND and OR plus the inverter. With these three all digital circuits can be constructed. That includes the XOR gate and the flip-flop. Other circuits like the multiplexer, demultiplexer, shift register, counter, memory and so on, are all built from the basic AND, OR and inverter.
Here's an example: Suppose you wanted to build a 7-segment display clock or timer. You can control (turn off or on) each segment independantly, or you could tie them all together and multiplex the data going to them. Multiplexing is the process of putting multiple pieces of information on the same wires, then seperating them out again at the other end.
Using this method alone, you can reduce the number of wires going to the display from 34 wires to 14. You could reduce them further by taking advantage of the fact that the driver circuit is nothing more than a repeating waveform, and construct a driver circuit which produces the same output with 3 wires (supply, ground and sync pulse) input. Then if that same circuit also drove the flashing colon, your total wire count is 10, seven plus three.
Here are some interesting links:
Check out these pages "All about circuits", or "How to hook up a Triac".
You can find data sheets as well as educational materials here at The University of Washington EE Stores.
Need to calculate the series resistor needed for an LED? Go here for the answer.
Go to Electromechanical Devices, Systems and Applications for interactive learning objects which focus on a broad range of electromechanical concepts.
If you would like to learn prefered soldering techniques, this link is for you.
Information on the microcontroller trainer can be found here.
Email: Russ Puskarcik