yes hp1729, now i have to write out all of the 16 functions and i don't know if i am doing it correctly when you have Xy+xy’+xy’+xy for a table would it be 1, 1, 0, 0?

 

yes hp1729, now i have to write out all of the 16 functions and i don't know if i am doing it correctly when you have Xy+xy’+xy’+xy for a table would it be 1, 1, 0, 0?

It would really help if you made an attempt to actually make a table, even if it is a partial table.

xy + xy' + xy' + xy

is the same as

xy + xy'

since xy + xy is the same as just xy and xy' + xy' is just the same as xy'.

If x is false, then both xy and xy' are false and the overall expression is false. But if x is true, then you know that either xy is true or that xy' is true. Hence, if x is true then the overall expression is true.

 

is there an insert table i didn't see one sorry about that

 

x y ƒ1
1 1 1
1 0 1
0 1 1
0 0 1

now i have to find out what minterm fits that function and how i was doing it was just putting in their compliments i think that is how i was doing it, for example Xy+xy’+x’y+x’y’ is what i put in for ƒ1

 

is there an insert table i didn't see one sorry about that

There is a [TABLE]blah blah [/TABLE] tag pair you can use. For some reason it is not documented in the basic BB Code Help screen (it's probably a third-party add on). There's lots of help online about it.

But just formatting a table in text, preferably with [CODE] tags (so that you have a monospaced font) is more than adequate.

 

x y ƒ1
1 1 1
1 0 1
0 1 1
0 0 1

like that?

 

x y ƒ1
1 1 1
1 0 1
0 1 1
0 0 1

now i have to find out what minterm fits that function and how i was doing it was just putting in their compliments i think that is how i was doing it, for example Xy+xy’+x’y+x’y’ is what i put in for ƒ1

This is fine.

The Boolean expression is

f(x,y) = 1 (or f(x,y) = True)

But the canonical (i.e., 'standard') SOP form is

f(x,y) = xy + xy' + x'y + x'y'.

These articles might be of interest to you:

http://www.allaboutcircuits.com/technical-articles/boolean-basics/

http://www.allaboutcircuits.com/technical-articles/boolean-identities/

There are several additional articles in this family that just haven't been written yet.

 

So is * the same as ^ and + is the same as v in boolean expressions?

 

So is * the same as ^ and + is the same as v in boolean expressions?

Well, what does the Boolean Basics article say about that?

Note that the carat '^' is not quite the same as the logic conjunction symbol

\(
\text{\^} \; \text{vs.} \; \wedge
\)

But for people using the math symbols with a standard keyboard, that's what they use.

However, for people using the engineering conventions, we use the carat to mean exclusive-OR.

So you need to be aware of the context of where you see it.

 

Well, what does the Boolean Basics article say about that?

Note that the carat '^' is not quite the same as the logic conjunction symbol

\(
\text{\^} \; \text{vs.} \; \wedge
\)

But for people using the math symbols with a standard keyboard, that's what they use.

However, for people using the engineering conventions, we use the carat to mean exclusive-OR.

So you need to be aware of the context of where you see it.

In the symbols page in the text editor is a plus sign with a circle around it that is often used in mathematical literature to represent exclusive-or. I believe I used it in my example (post #12):

x ⊕ y means "x exclusive-or y". This function is true if x = 1 or y =1, but is false if x = y.

 

In the symbols page in the text editor is a plus sign with a circle around it that is often used in mathematical literature to represent exclusive-or. I believe I used it in my example (post #12):

x ⊕ y means "x exclusive-or y". This function is true if x = 1 or y =1, but is false if x = y.

The TS appears to just be using text-based symbols.

I have never found a key board that has the + symbol surrounded by a circle.

They might well exist.

I'm also not aware of a programming language that has that symbol in its source alphabet, but again one might well exist.

The plus-with-circle is definitely useful for hand-written stuff and is often used in engineering texts and publications. I don't know about math literature, but I believe that formal logic has a different symbol for what we call exclusive-OR, namely \(\underline{\vee}\).

EDIT: Finally found the latex command that the MimeTex engine recognizes.

 

The TS appears to just be using text-based symbols.

I have never found a key board that has the + symbol surrounded by a circle.

They might well exist.

I'm also not aware of a programming language that has that symbol in its source alphabet, but again one might well exist.

The plus-with-circle is definitely useful for hand-written stuff and is often used in engineering texts and publications. I don't know about math literature, but I believe that formal logic has a different symbol for what we call exclusive-OR, namely \(\veebar\).

The only computer language I can think of might be Iverson's APL since it was based on selectric typewriters with interchangeable balls.

 

The only computer language I can think of might be Iverson's APL since it was based on selectric typewriters with interchangeable balls.

Interesting. So how was the source code stored? It would have to have encode which ball was used for a given character (or so it would seem).

 

Interesting. So how was the source code stored? It would have to have encode which ball was used for a given character (or so it would seem).

Or are you saying that there was one particular ball that was always used for APL programs?

 

I'm a bit fuzzy on the details, but I think there was an APL ball for the Selectric typewriter, and the special characters were mapped into blank spaces in the EBCDIC character set which was always an 8-bit character set.
https://en.wikipedia.org/wiki/EBCDIC
http://www.computerhistory.org/collections/catalog/102696478

Table 3-2 shows the mapping for the APL character Set
https://books.google.com/books?id=-2mrCAAAQBAJ&pg=PA48&lpg=PA48&dq=Characters+on+the+APL+ball+for+a+selectric+typewriter&source=bl&ots=qAyGxJcKAh&sig=BptEVuUQLkSkJMBIn3THa06p4lA&hl=en&sa=X&ved=0ahUKEwjbrMCai9rJAhUCYyYKHR8ZBOwQ6AEITzAI#v=onepage&q=Characters on the APL ball for a selectric typewriter&f=false

Alas no evidence of a dedicated exclusive-or symbol
https://en.wikipedia.org/wiki/APL_syntax_and_symbols

 

That would make sense.