4 bit propositional logic

4 bit logic


We know from basic proposition logic,

That 0&0=0, and 0|1=1.


Now let's try 4 bit logic basics.

In written form:


0=0

1=1

2=2

3=3


We know the basics:

0&0=0

0&1=0

1&0=0

1&1=1


Now for &:

2&0=0

2&1=0

2&2=2

2&3=3&2

3&2=2&3


3&0=0

3&1=0

3&2=2&3

3&3=3


--


Now for or denoted by | (inclusive):


0|0=0

0|1=1

1|0=1

1|1=1


2|0=2

2|1=1|2

2|2=2

2|3=3|2


3|0=3

3|1=1|3

3|2=2|3

3|3=3


--

Lets denote exclusive or with /


0/0=0

0/1=1

1/0=1

1/1=0


2/0=2

2/1=1/2

2/2=0

2/3=3/2


3/0=3

3/1=1/1

3/2=2/3

3/3=0


--

Now for not:


!0=1|2|3

!1=0|2|3

!2=0|1|3

!3=0|1|2


--


If then denoted by >


0>0=1

0>1=1

1>0=0

1>1=1


Then:


0>2=0|1|3

0>3=0|1|2


1>2=0|1|3

1>3=0|1|2


2>0=0|1|3

2>1=0|2|3

2>2=0|1|3

2>3=0|1|2


3>0=1|2|3

3>1=0|2|3

3>2=0|1|3

3>3=1|2|3


Comments

  1. PsimythDecember 21, 2022 at 5:48 PM

    So lets do a little comparison on first glance:

    0>2=2>0
    3>0=3>3

    and

    0>3=1>3=2>3

    Etc.

    ReplyDelete
  2. PsimythDecember 21, 2022 at 9:58 PM

    I have a feeling this logic will make computer's (cpu's) twice as fast at the cost of twice the memory (ram).

    Also it could be improved to 8 bit logic to make current cpu's 4 times as fast at 4 times the cost of ram.

    There is a meta-logic to this logic which I hope to write about. It should expand to maximum available ram, with maximal attainable speed.

    ReplyDelete
    Replies
    1. PsimythDecember 21, 2022 at 10:06 PM

      Economically it doesn't make much sense, but speed increase does not follow Moore's Law anymore, so its worth a shot.

      Delete

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