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It happens I've got away without using one in many circuits, but just occassionaly I get stung by my laziness. And when said circuits malfunction, they malfunction intermittently, making debugging about as joyful as root canal surgery. Good practices own
The transistor isn't needed to drive only 4 LEDs. The 555 has an output current of up to 200mA.
Even if the transistor is used it doesn't need a base-emitter resistor because the output low voltage of a 555 is typically 0.1V which will certainly turn off the transistor.
If the output of a 555 is driving a PNP transistor then a voltage divider must be used to turn off the transistor because the output high voltage of a 555 is about 1.2V less than the positive supply.
I call it "a supply bypass capacitor". It keeps the supply at a low impedance so its voltage doesn't jump up and down when the load current changes. It also supplies current when the load demands current but the supply is too weak to supply it. A 555 draws a current spike of 400mA each time the output switches. The datasheet of the 555 says to use a supply bypass capacitor to supply the momentary current to protect other circuitry that is using the same supply.
Sounds like you are talking about the capacitor in the lower left corner. If so, Im glad to finally hear the reason for that capacitor's existance.Clayton
No, that is the timing capacitor, the whole reason for the 555's existance. Were it not for that capacitor's repeated charging and discharging through the accompanying resistors, the 555 would not perform as an astable multivibrator. There are many good tutorials available that explain the inner working of the 555 in detail.
By itself, just blinking an LED, a 555 can live without a bypass cap. But put it into a circuit, say with a 7490 counter, without a bypass cap and all kinds of crazy things can happen. It's definately best to use one.
No, the best place to put it is between pin 8 and GND.
Batteries and power supplies are not really zero impedance sources, especially if they have long wires (which have resistance and inductance) between them and your circuit. The bypass capacitor provides a local low impedance, so that current transients, which the 555 is famous for, can find an easy path to GND. Otherwise, the transients will cause big voltage spikes on the power pins, which can screw up the operation of the circuit.
Every circuit you build which is more complex than a battery and a light bulb (a little hyperbole never hurt anyone) should have at least one, and maybe many, in the case of a big board.
No.
The capacitor in the lower left corner of the schematic is the timing capacitor that charges with R1 and R2 in series then dischargges with only R2.
The circuit doesn't have a supply bypass capacitor which should be about 100uF for this circuit and be connected from pin 8 of the IC and to ground at pin 1.
If the circuit is powered by a 9V battery then sometimes it won't work without a supply bypass capacitor because the supply voltage would be bouncing up and down so much. If it is powered by a car battery with very short wires then the bypass capacitoer wouldn't be needed.
The output transistors of the 555 have a very high current surge from the supply that causes the supply voltage to drop. The supply bypass capacitor supplies that momentary current so the voltage doesn't drop too low. If the voltage is allowed to drop too low then circuits don't work.
The bypass capacitor keeps the power supply voltage constant. If a series resistor feeds the 555 instead then the voltage will drop when it and the load draw current. Then the supply voltage would bounce up and down a lot.
There is not a surplus of voltage. The supply bypass capacitor stops the voltage from dropping too low when a high current pulse tries to reduce it.
I use a 100uF supply bypass capacitor for some battery powered electronic circuits because it can supply 400mA for about 1.2milli-seconds.The output of a 555 switches in 100ns so the voltage won't drop much with 100uF holding it up. Use only 10uF and the voltage might drop to half.
For audio circuits I use 1000uF. For logic circuits I use a 0.1uF ceramic disc capacitor. For FM radio transmitter circuits I use a 1000pF ceramic disc capacitor.
All electronic circuits need supply bypass capacitors. On logic circuits that used old TTL ICs a 0.1uF ceramic disc supply bypass capacitor was used at each IC. Microprocessors also need one.
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I've got away without using one in many circuits, but just occassionaly I get stung by my laziness. And when said circuits malfunction, they malfunction intermittently, making debugging about as joyful as root canal surgery. Good practices own 
