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When two flip-flops are triggered from the same clock, or if one of the outputs is used as an input, the input and output signals can sometimes get confused A master slave (M/S) flip-flop overcomes this bugaboo by storing inputs before allowing the outputs to change state An M/S flip-flop consists of two R-S flip-flops in series The first flip-flop is called the master, and the second is called the slave The master flip-flop functions when the clock output is high, and the slave acts during the next low portion of the clock output This time delay prevents confusion between the input and output of the circuit

Again, let s multiply out the right sides of the binomial-squared equations When we do that, we obtain y = a 2x 2 + 2abx + b 2 and y = a 2x 2 2abx + b 2 Setting the right sides equal gives us the mixed quadratic a 2x 2 + 2abx + b 2 = a 2x 2 2abx + b 2

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When we subtract the quantity (a 2x 2 + b 2) from each side, we get 2abx = 2abx We can add 2abx to each side and then divide through by 4ab (which is legal because we ve been told that a 0 and b 0, so we can be sure that 4ab 0) When we do that, we obtain x = 0 as the only root of the mixed quadratic We can substitute this value for x into the original equations, obtaining y = b2 in both cases Therefore, the system has the single solution (0,b2)

The J-K flip-flop works just like an R-S circuit, except that it has a predictable output when the inputs are both 1 Table 30-9 shows the input and output states for this type of flip-flop The output changes only when a triggering pulse is received The symbol for a J-K flip-flop is shown in Fig 30-7 It looks just like the R-S flip-flop symbol, with the addition of a third (trigger) input, labeled T

Epipolar Navigation Epipolar navigation works by evaluating the way an image changes as viewed from a moving perspective Suppose that you are piloting an aircraft over the ocean The only land in sight is a small island The on-board computer sees an image of the island that constantly changes shape Figure 30-15 shows three sample sighting positions (A, B, C) and the size/shape of the island as seen by a machine vision system in each case The computer has the map data, so it knows the true size, shape, and location of the island The computer compares the shape and size of the image it sees at each point in time, from the vantage point of the aircraft, with the actual shape and size of the island from the map data From this, the computer can ascertain the altitude of the aircraft, its speed and direction of movement relative to the surface, its latitude, and its longitude Log Polar Navigation In log polar navigation, a computer converts an image in polar coordinates to an image in rectangular coordinates The polar radius is mapped onto the vertical rectangular axis, and the polar angle is mapped onto the horizontal rectangular axis Radial coordinates are unevenly spaced in the polar map, but are uniform in the rectangular map During the transformation, the logarithm of the radius is taken to maximize the geographical area that the system can observe As a result of this logarithmic transformation (that s where the log comes from in the term), long-distance resolution is sacrificed, but the close-in resolution is enhanced The so-called log polar transform distorts the way a scene appears to human observers, but translates images and motions into data that can be efficiently dealt with by a computerized scanning system Loran The term loran is an acronym derived from the words long range navigation Loran is one of the oldest electronic navigation schemes, and is still used by some ships and aircraft The system employs RF pulse transmission at low frequencies from multiple transmitters at specific geographic locations In loran, a computer on board a vessel can determine the location of the ship by comparing the time difference in the arrival of the signals from two different transmitters at known locations Based on the fact that radio waves propagate at the speed of light in free space (approximately 299,792 km/s or 186,282 mi/s), it is possible to determine the distance to each transmitter, and from this, the location of the ship relative to the transmitters In recent years, loran has been largely supplanted by the Global Positioning System (GPS).

Question 27-8

Some digital circuits can be programmed to change state every so-many clock pulses Such a circuit is called a counter It is also often called a divider, because if the output

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