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In schematic diagrams, a flip-flop is usually shown as a rectangle with two or more inputs and two outputs If the rectangle symbol is used, the letters FF, for flip-flop, are printed or written inside at the top The inputs of an R-S flip-flop are labeled R (reset) and S (set) The outputs are Q and Q (Often, rather than Q, you will see Q , or perhaps Q with a line over it) As their symbols imply, the two outputs are always in logically opposite states The symbol for an R-S flip-flop is shown in Fig 30-5

Part Three 527 Answer 27-6

Fluxgate Magnetometer When conventional position sensors do not function in a particular environment for a mobile robot, a fluxgate magnetometer can be used This system employs sensitive magnetic receptors and a

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The best approach here is to multiply out the right sides of both of the binomial-squared equations, obtaining the quadratics in polynomial standard form When we do that, we get y = x 2 + 2x + 1 and y = x 2 2x + 1 Mixing the right sides of these quadratics gives us x 2 + 2x + 1 = x 2 2x + 1 Subtracting the quantity (x 2 + 1) from each side, we obtain 2x = 2x We can add 2x to each side and then divide through by 4 to get x = 0 as the sole root of this mixed quadratic When we substitute this value for x into either of the original equations, we get y = 1 Therefore, the system has the single real solution (0,1)

In an R-S flip-flop, if R 0 and S 0, the output states do not change; they stay at whatever values they re already at If R 0 and S 1, then Q 1 and Q 0 If R 1 and S 0, then Q 0 and Q 1 That is, the Q and Q outputs will attain these values, no matter what states they were at before But if S 1 and R 1, things get bizarre The flip-flop becomes unpredictable Because of this, engineers avoid letting logic ls get into both inputs of an R-S flip flop You want logic, not absurdity! Table 30-8 is the truth table for an R-S flip-flop

Question 27-7

microcomputer to sense the presence of, and detect changes in, an artificially generated magnetic field Navigation within a room can be done by checking the orientation of magnetic lines of flux generated by electromagnets in the walls, floor, and ceiling of the room For each point in the room, the magnetic flux lines have a unique direction and intensity There is a one-to-one correspondence between the magnetic flux intensity/direction and the points within the robot s operating environment This correspondence can be represented as a two-variable mathematical function of every location in the room The robot controller is programmed to know this function This makes it possible for the machine to pinpoint its position with extreme accuracy, in some cases to within a few millimeters

Consider the following pair of quadratic equations as a two-by-two system: y = (ax + b)2 and y = (ax b)2 Where a and b are real numbers, neither of which are equal to 0 How can we find the real solutions of this system

An R-S flip-flop output changes state as soon as the inputs change If the inputs change at irregular intervals, so will the outputs For this reason, the aforementioned circuit is sometimes called an asynchronous flip-flop A synchronous flip-flop changes state only at certain times The change-of-state times are determined by a circuit called a clock The clock puts out a continuous train of pulses at regular intervals There are several different ways in which a synchronous flip flop can be triggered, or made to change state In static triggering, the outputs can change state only when the clock signal is either high or low This type of circuit is sometimes called a gated flip-flop In positive-edge triggering, the outputs change state at the instant the clock signal goes from low to high, that is, while the clock pulse is positive-going The term edge triggering derives from the fact that the abrupt rise or fall of a pulse looks like the edge of a cliff (Fig 30-6) In negative-edge triggering, the outputs change state at the instant the clock signal goes from high to low, or when the pulse is negative-going

Answer 27-7

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