# Notes

## Notes - notes.io

Binary digits
Digital electronics uses circuits that have two states, which are represented by two different voltage levels called HIGH and LOW. The voltages represent numbers in the binary system. One byte is 8 bits.

Digital waveforms
Digital waveforms change between the LOW and HIGH levels. A positive going pulse is one that goes from a normally LOW logic level to a HIGH level and then back again. Digital waveforms are made up of a series of pulses. These waveforms carry binary information and these waveforms represent sequences of bits. HIGH means 1 and LOW means 0. Each bit in a sequence occupies a defined time interval and thats called the bit time. A positive going pulse is one that goes from a normally LOW level to a HIGH level and then back again. A negative going pulse is one that goes from a normally HIGH level to a LOW level and then back again. An idealised pulse is a pulse that changes state instantaneously, in the real world this does not happen. In a positive going pulse the first rise is called the RISING edge and also the LEADING EDGE. The second change in gradient or fall, is called the FALLING edge or TRAILING edge. In negative going pulses this is exactly opposite, the first edge is called the FALLING edge or LEADING EDGE and the second edge is called the RIDING or TRAILING edge.

Timing diagrams
These state changes don’t happen by them selves, they are usually in a system that is clocked (learn more in sequential logic and memory logic). It shows the differences between information carried in different waveforms by using timing diagrams. At the top you can see the clock which has a periodicity from a LOW state to a HIGH state and underneath you can see a number of waveforms usually labelled by A, B and C with changes in their logic states accordingly.

Data transmission
Data can be transmitted by either serial transfer or a parallel transfer. Serial transfer is when one ‘wire’ so to speak changes state and sends the binary information one after another. Parallel transfer is when multiple wires are connected between two devices and the state of each wire changes accordingly at the same time effectively multiplying the operating speed by 8.

AND gate (semicircle square, represented by a .) both inputs need to be HIGH and the output will be HIGH
OR gate (arrow looking, represented by a + sign) only one input needs to be HIGH and the output will be HIGH
NOT gate or inverter (A line drawn over the input or output) inverts any output from HIGH to LOW and from LOW to HIGH
NAND gate (and and not gate combined, AND symbol (.) with a line drawn over it) exactly the same as an AND gate but with exactly opposite outputs
NOR gate (or and not gate combined, OR symbol (+) with a line drawn over it) exactly the same as an OR gate but with exactly opposite outputs.
Exclusive OR (XOR) gate (arrow with a line behind it or circle with a plus sign in it) one input or the other input has to be HIGH so the output is high but if both inputs are HIGH the output will be LOW

Demogran’s theorem
If you invert he output of any gate it is the same as using an opposite TYPE of gate but inverting the inputs.
Example:
A.B == A + B
A+B == A.B
Can confirm with truth tables

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