74154 4 line to 16 line decoder

[ravenprp]

Hi.. my HW question reads:

Design a circuitboard based on a 74154 4 line to 16 line decoder that will output a HIGH henever the 4 bit binary is greater than 12 and output a low when it is less than 12 or equal to 12.

http://pdf1.alldatasheet.com/datasheet-pdf/view/7826/NSC/74154.html

I have the IC drawn on my paper, and what I have done is for the inputs from 13-15, I have it going to an NAND gate.

so if one of those inputs is an active LOW input, then once gates 13, 14, 15 go through the NAND with the values 0, 1, 1, (respectively), it will output a "1" or "HIGH"... Now, for gates 0 - 12... I'm using a NOR gate.

Now, I connect the NAND gate and the NOR gate into a XOR gate.Brief recap: gates 13-15 go into a NAND. That output goes into one input for an XOR. Then gates 0-12 go into a NOR. Then that output goes into one input for the same XOR as above.

 

[berkeman]

I'm not sure that I understand your solution. The outputs of the 4:16 demux represent the count of the input lines, right? So if you want to output a 0 when the input count is 12 or more, what can you put on lines 12-15 to output a 0 if any input is a 1, and output a 0 otherwise?

 

[ravenprp]

The second input for the XOR is a constant "1" input. This will ensure that the output of the XOR will be a "1" or "HIGH" only when the input from gates 13-15 is a "1" and the input from gates 0-12 is a "0". This satisfies the condition of the output being "HIGH" only when the 4 bit binary is greater than 12.

For the output to be "LOW" when the 4 bit binary is less than or equal to 12, we can simply use an inverter on the output of the XOR gate. This will result in the output being "LOW" when the XOR output is "1" and "HIGH" when the XOR output is "0", fulfilling the desired condition.

Overall, this circuit design utilizes the NAND and NOR gates to create a condition where the output will be "HIGH" only when the input is greater than 12 and "LOW" when the input is less than or equal to 12. The XOR gate acts as a comparator to compare the inputs and produce the desired output.