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Lab Report #3
05 February 2002
Nicolo Africa
Jessica Sugay
In the laboratory activity, we wanted to modify our existing setup so that it would count from zero to six, instead of nine. To do this, we made use of the 0110 blackbox. This "box" (which isn’t literally a box, but a setup consisting of two chips) is specifically designed (by ourselves) to send out an output of 1 everytime and only when the binary input through it is 6 (= 0110 in binary).
This function can be represented in a truth table (Fig.2). We started out by deriving an equation from this table (Fig.3). From there, we were able to obtain the needed circuit for the desired output (Fig.4). (NOTE: We had to modify the circuit so as to use only NAND and NOR gates, since these are the only types supported by the two chips of the black box—the 7400 and 7402)
As we learned from the previous experiment, the 7490 chip (Fig.5) is a decade counter that counts from 0 to 9 (in binary) cyclically in its natural state. Its pins 12, 9, 8 and 11 correspondingly represent four bits in a binary number (QA,QB, QC and QD). It is also important to note in this experiment that when pins 2 and 3 (R01 and R02) of the 7490 are both brought to high, the count resets to zero. Pins 6 and 7, which when either is brought to high sets the count to nine, are brought to ground since we desire to count only up to six.
The 7400 chip contains four NAND gates (Fig.6), while the 7402 chip contains four NOR gates (Fig.7). The combination of these two, which is the blackbox, is used to implement the circuit in Fig.4.
In a nutshell, the blackbox (Fig.8) takes in the four bit binary number which the 7490 outputs, and when the value six (0110) is recognized, tells the 7490 to start once again from zero. To be more specific (following the circuit diagram), the outputs of pins 12 and 11 (QA and QD) of the 7490 were sent to two inputs (pins 2 and 3) of a NOR gate in the 7402. On the other hand, the outputs of pins 9 and 8 (QB and QC) of the 7490 were sent to two inputs (pins 1 and 2) of a NAND gate in the 7400. The output here (pin 3) is NANDed with itself through input pins 4 and 5, and then the new output (at pin 6) is NANDed with the output from pin 1 of the 7402 NOR gate through pins 9 and 10 of the 7400. Once again, the output (pin 8) is NANDed with itself through pins 12 and 13 of the 7400. The final output from pin 11 is sent back to the 7490 through input pins 2 and 3 (R01 and R02). When a number other than 6 is fed through the blackbox, the output is zero and the count continues. However, if 0110 is received, the output is 1 (see Fig.4), R01 and R02 of the 7490 are brought to high, and thus, the count resets to zero right after six. (Note: We do not see the six because it lights up and resets to zero within a matter of nanoseconds, as soon as it is ‘identified’ by the blackbox.)
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