www.nortonkit.com  18 अक्तूबर 2013  
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Combinational Logic:  [Basic Gates] [Derived Gates] [The XOR Function] [Binary Addition] [Negative Numbers and Binary Subtraction] [Multiplexer] [Decoder/Demultiplexer] [Boolean Algebra] 
Sequential Logic:  [RS NAND Latch] [RS NOR Latch] [Clocked RS Latch] [RS FlipFlop] [JK FlipFlop] [D Latch] [D FlipFlop] [FlipFlop Symbols] [Converting FlipFlop Inputs] 
Alternate FlipFlop Circuits:  [D FlipFlop Using NOR Latches] [CMOS FlipFlop Construction] 
Counters:  [Basic 4Bit Counter] [Synchronous Binary Counter] [Synchronous Decimal Counter] [Frequency Dividers] [Counting in Reverse] [The Johnson Counter] 
Registers:  [Shift Register (S to P)] [Shift Register (P to S)] 
The 555 Timer:  [555 Internals and Basic Operation] [555 Application: Pulse Sequencer] 
Decimal and Shorter Counts 

States  Count 
To create a decimal counter, we need to find a way to cut the counting sequence short. The Truth Table to the left shows the actual counting sequence we need. Note that the counting sequence is exactly the same as for the binary counter we saw on the previous page, up through a count of 9. At that point, where the binary counter would continue on to a count of 10, the decimal counter must reset itself to a count of 0. In this sequence, flipflops A and C are no problem. Their next states will both be logic 0 whether the next count is 10 or 0. However, flipflop B would normally switch from logic 0 to logic 1, and must be prevented from doing so. At the same time, flipflop D, which is at logic 1, must be made to switch back to logic 0. Hmmmm. Since flipflop D is a logic 1 for only two counts, and only flipflop A will change state going from count 8 to count 9 in any case, perhaps we can use the D and D' outputs, with gates, to force the desired change in sequence. This is in fact the case, as shown in the demonstration below. Note that we have applied different signals to the J and K inputs of flipflop D. This is perfectly acceptable, and allows us to reset this flipflop under the control of a simple twoinput AND gate. 


D  C  B  A  
0  0  0  0  0  
0  0  0  1  1  
0  0  1  0  2  
0  0  1  1  3  
0  1  0  0  4  
0  1  0  1  5  
0  1  1  0  6  
0  1  1  1  7  
1  0  0  0  8  
1  0  0  1  9 


Now that we've seen counting sequences other than binary, new questions arise: Can we generate other counting sequences for special purposes? And are there other uses for counting circuits than numeric counts? We'll explore these questions on the next page.


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