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Clocked Logic:How counters work... (LESSON 1)


The RS Flip-Flop

THE RS FLIP-FLOP

    This is the Set-Reset Flip Flop logic block. Although it is called RS, it is said to stands for Set-Reset*. You can see that the inputs of one NOR GATE receive from the output of another. Note the point where the two wires cross (make an X). This is not a point of connection. It could, alternatively, be drawn like this:
alternative drawingIn this form the wires do not cross and it is clear that there is no direct connect between the two outputs. However, in more complex circuits it is sometimes not possible to find an "alternative" path and the lines have to cross.  The rules for connections are illustrated below.



    The special ability of an RS Flip Flop is to "remember" the last state it was set in. NEW TERM: SET means changed to the value of 1 and RESET means changed to 0. In otherwords, the RS flip flop is a 1 bit memory. It can retain the state of either a 1 or a 0. A bit is like a digit, only it is for binary. We use the decimal number system, also known as base 10. We have 10 numbers {0,1,2,3,4,5,6,7,8,9}. In binary there are only two numbers to use {0,1} A single "digit" in binary is called a bit. You may have heard the term byte before or mega byte. One byte is equal to 8 bits and a MB is equal to about a million bytes. With a little modification 8 RS Flip Flops could be used to make a 1 byte memory!

An example of a bit (  0  )
An example of a byte (  01010101   )

To learn more about the binary number system CLICK HERE

Lets assume that the R and S values for the RS flip flop are both 0. What would the Q and compliment of Q be? Lets try to use the skills from the previous lesson to figure it out...

RS flip flop with 0 and 0 for inputs

It seems like there is some information missing. We can't determine the output of either gate since the gates take inputs from the outputs!!
However, we could try using the truth table of the NOR GATE as a guide, we know that if 1 or both of the inputs is a 1 then the output has to be 0. But, since the value given for R and S is 0 we can't mathematically determine the result of either gate. It could be 1 or 0. Electronically, though, what would happen...? Because of slight imperfections in the transistors themsevles along with electrical characteristic variations in the wires that connect them one gate will turn on slightly faster than the other, maybe only by nanoseconds.

gate 1 takes input from gate 2's output

Lets  say  gate 1 turns on first. Since gate 2 is still off, it has an output of 0. Gate 1 takes the output value of 0. Since Gate 1 has two 0's for outputs, it's output becomes 1, based on its truth table. Meanwhile... gate two powers up. It takes the output from gate 1 (1) and its output becomes 0, which it was when it was "off". The loop stops and the circuit stabilizes. This is called a stable state. It will remain in this state unless there is a loss of power or S/R are changed.

within fractions of a second the powered up circuit stabilizes    Circuit stabilized...

Every time you power up this circuit it could initialize in a different state, because of electrical variations. Q will always be the opposite of opposite of Q or vice versa, however. When doing these circuits on paper, you have to "make up" a state it starts in. After that you can calculate the changes based on the inputs.

Here is the Truth table for the RS Flip Flop. You should be able to derive this from the circuit on paper...

S
R
Q
compliment of Q
0
0
Stays the same
Stays the same
0
1
0
1
1
0
1
0
1
1
0 - disallowed state
0 - disallowed state


memory light

A circuit like this could be built... When switch A is pressed down the LED lights, nothing special yet. When switch A is released, however, the light continues to glow! The R-S Flip Flop "remembered". Now press button B. The LED goes off and if there was an LED attached to the other gate it would now turn on. When button B is released the LED stays on. Once again, the circuit retain it new state. If both buttons are pressed both LEDs would light, but this is a disallowed state because the circuit will not retain the memory of two LEDs on, As soon as the buttons are released, the circuit will return to some unpredictable, but stable, state. If the same button is pressed twice or more in a row, nothing happens.



Click on image above for an interactive simulation



    The open switch from the previous example represented a low state and a closed switch was high. Electrically this may not be the case and the input to the gate might have to be "pulled-down" low with a resistor. A high ohm resistor between the input and ground would fix this problem. Notice when the Q and actually change state, thisis important. If R and S are held low (0) the states of the "Qs" remain unaltered. As soon as a high signal comes in, the state changes. This is called high or positive logic. A functionally equivalent circuit could be built that only reacted to the incoming of a low state (negative logic).
    The only structural difference is that the circuit is built with NAND GATES, instead of NOR GATES...

RS Flip-Flop using NAND gates


   
    Below is the truth table for the low edge triggered RS Flip-Flop
S
R
Q
compliment of Q
0
0
0 - disallowed state 0 - disallowed state
0
1
1
0
1
0
0
1
1
1
Stays the same
Stays the same


    On this style of RS Flip-Flop, S and R would normally be held HIGH, to maintain the state.  If  S momentarily dropped low  Q would  go high and would go low. If R were to momentarily drop low the opposite would happen. On the RS Flip-Flop built with NOR gates, from the previous example, the change happened from the change to high rather than the change to low.

To better illustrate this idea, consider the following example.


    The button labeled "type 1" triggers an alert menu to popup when the mouse button goes down. The type 2 button triggers the event when the mouse button is released. Try it. This is similar to the difference between positive and negative triggered logic. This concept is important when interfacing different logic blocks. Lets say you have a device that outputs high when the temperature is above 100 degrees Celsius and another device that sounds a buzzer when the input goes low. With those specifications, the two devices would not be readily interfacable and an inverter would have to be used to bridge the two together.





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Gates: Lesson 3
Clocked Logic: Lesson 1
  Clocked Logic: Lesson 2


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