[EMS Discuss] Logic Diagram Challenge

Mark Danburg-Wyld danburgwyld at gmail.com
Thu Jan 16 09:19:23 PST 2014


I don't know what constitutes a gate, but I do know my symbolic logic...
>>> def outputs(a, b):
    c = a & b
    d = a & ~c
    e = b & ~c
    print c, d, e

>>> outputs(0, 0)
0 0 0
>>> outputs(0, 1)
0 0 1
>>> outputs(1, 0)
0 1 0
>>> outputs(1, 1)
1 0 0
>>>

So is that 3 gates, or 5?


On Thu, Jan 16, 2014 at 8:58 AM, Mr. Clif <clif at eugeneweb.com> wrote:

>  Way to go Darrell!
>
> That sounds perfectly normal except that if I understand you correctly you
> would say that the output of the AND gate propagates into the inputs of the
> XORs.
>
> After I went to bed last night I realized that with the MC10H104 I can
> also do it with three of the four gates in just that one package. So not
> only can I do it in three gates I can also do it without buying several
> different gate packages.
>
> Ok Weston you've got two guys that claim to have solved it in three gates!
> :-p what now?
>
>     Clif
>
>
> On 01/16/2014 03:21 AM, Darrell Perko wrote:
>
>
> I think I have a solution using two XOR and one AND, though the AND is
> both an output and it feeds back into the input of the XORs.  That seems
> like it could cause brief illegal outputs states.
>
> On 1/15/2014 11:49 PM, Mr. Clif wrote:
>
> Ok here is a Quad and gate part that you can do it with just one package:
>
> MC10H104
>
> there may be others.
>
>     Clif
>
> On 01/15/2014 10:40 PM, Mr. Clif wrote:
>
> Ok ;-)
>
> So when you say that "inverting operations count as NOT gates" do you
> mean that they aren't counted as gates or that they are "Not operations"
> implemented as gates, which of course they are?
>
> One issue with doing this your way in hardware, is that you need three
> different types of gates unless you are doing it in an FPGA or the like.
>
> Here it is in a shorter logical expression:
> C = A & B; D = !C & A; E = !C & B
>
> I have another way that uses four of the same kind of gate though they may
> be some what uncommon. ;-)
>
>     Ciao,
>     Clif
>
> On 01/15/2014 10:04 PM, Weston Turner wrote:
>
>  From a more rigorous or theoretical standpoint, the inverting operations
> count as NOT gates. But I guess I didn't say that inverting equals a NOT.
> In any case, my four gate solution doesn't use them. I'll represent it here
> in Python using four binary bitwise operators, one AND, one OR, and two
> XORs.
>
> A and B are anded to make C
> A and B are ored  together into the temp variable t
> t is xored with B to make D
> t is xored with A to make E
>
>  The operations are color coded below. Can this be done with fewer
> operations?
>
> Python 2.7.3 (default, Nov 11 2012, 18:06:39)
> >>> *A, B = 0, 0*
> >>> t = A | B; C = A & B; D = B ^ t; E = A ^ t
> >>> C, D, E
> *(0, 0, 0)*
> >>> *A, B = 0, 1*
> >>> t = A | B; C = A & B; D = B ^ t; E = A ^ t
> >>> C, D, E
> *(0, 0, 1)*
> >>> *A, B = 1, 0*
> >>> t = A | B; C = A & B; D = B ^ t; E = A ^ t
> >>> C, D, E
> *(0, 1, 0)*
> >>> *A, B = 1, 1*
> >>> t = A | B; C = A & B; D = B ^ t; E = A ^ t
> >>> C, D, E
> *(1, 0, 0)*
>
>  Cheers,
>  Weston
>
>
>
> On Wed, Jan 15, 2014 at 8:42 PM, Mr. Clif <clif at eugeneweb.com> wrote:
>
>> Sure I can do it in three but two of the gates have to have one inverting
>> input each. Since gates often come in quad packs it might be nice to find a
>> circuit that would use all four in a pack. Though if it helps my fourth
>> gate is just an inverter and there are often left over ones from other
>> packages.
>>
>>     Clif
>>
>>
>>
>>
>>
>> On 01/15/2014 07:42 PM, Weston Turner wrote:
>>
>>>  I'm wondering if anyone can implement this logic table with less than
>>> four gates...
>>>
>>> A B | C D E
>>> -------------
>>> 0 0 | 0 0 0
>>> 0 1 | 0 0 1
>>> 1 0 | 0 1 0
>>> 1 1 | 1 0 0
>>>
>>> I figured out a way to implement it with four gates but I'm wondering if
>>> it can be reduced further...
>>>
>>> And if you can only figure out a way to do it with four, then I'm
>>> curious to see if you arrived at the same solution I did.
>>>
>>> Regards,
>>> Weston
>>>  _______________________________________________
>>> Discuss mailing list
>>> Discuss at eugenemakerspace.com
>>> http://eugenemakerspace.com/mailman/listinfo/com.eugenemakerspace.discuss
>>>
>>
>>
>
>
>
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