Logic Gates and there link with binary

[gizzemoto]

I have moved over from analogue electronics to digital electronics, Is there a trick to remmembering the 6 basic gates and there logic How are these linked to binary

 

[phalanx]

The only trick I know is to just remember the truth tables for the 3 basic gates.

AND: 0&0=0; 1&0=0; 0&1=0; 1&1=1
OR: 0|0=0; 1|0=1; 0|1=1; 1|1=1
XOR: 0 xor 0=0; 1 xor 0=1; 0 xor 1=1; 1 xor 1=0

The output of the other three gates (NAND, NOR, XNOR) are just the opposite of their respective matches.

The binary nature of these parts is due to the fact that they can only be in one of two states: HIGH or LOW. There is no inbetween. Because only two states exist, the system is binary.

 

[ljcox]

I have moved over from analogue electronics to digital electronics, Is there a trick to remmembering the 6 basic gates and there logic How are these linked to binary

The attachment may help you.

 

[Roff]

The attachment may help you.

Thank you, Augustus DeMorgan.

 

[ljcox]

Thank you, Augustus DeMorgan.

Yes, and to Norman McLeod with whom I used to work who pointed this out to me many years ago.

 

[Pommie]

I thought the names themselves gave the game away.

If A=1 AND B=1 then output = 1
If A=1 OR B=1 then output = 1

XOR is the slightly tricky one but if the inputs are exclusive (different) then the output = 1. This is why you can only ever have a 2 input XOR gate.

If there is a N in front of the name then replace "=1" with "=0"

Matbe the OP's first language isn't English.

Mike.

 

[Roff]

I thought the names themselves gave the game away.

If A=1 AND B=1 then output = 1
If A=1 OR B=1 then output = 1

XOR is the slightly tricky one but if the inputs are exclusive (different) then the output = 1. This is why you can only ever have a 2 input XOR gate.

If there is a N in front of the name then replace "=1" with "=0"

Matbe the OP's first language isn't English.

Mike.

Here is the truth table for a 3-input XOR.

 

[ljcox]

I thought the names themselves gave the game away.

If A=1 AND B=1 then output = 1
If A=1 OR B=1 then output = 1

Mike.

0 and 1 can be confusing since in positive logic, 1 = high & 0 = low but in negativelogic, 0 = high & 1 = low.

So it is less confusing to use "active high" and "active low".

eg. when a NAND gate is used as an AND gate it has active high inputs and an active low output. Or if it is used as an OR gate, it has active low inputs and an active high output.

 

[ljcox]

Here is the truth table for a 3-input XOR. I think the definition extends to "the output is true if one and only one input is true".

That's interesting Ron, but I would have thought that the output of a true 3 input XOR would be 1 when only one of the inputs = 1, but the truth table in the paper also has the output = 1 when A, B & C are all equal to 1.

In relay logic there is a "one only chain" which is active (ie. there is a connection through it) when one and only one of a group of relays is operated, ie. a true XOR.

 

[Roff]

That's interesting Ron, but I would have thought that the output of a true 3 input XOR would be 1 when only one of the inputs = 1, but the truth table in the paper also has the output = 1 when A, B & C are all equal to 1.

In relay logic there is a "one only chain" which is active (ie. there is a connection through it) when one and only one of a group of relays is operated, ie. a true XOR.

I didn't look far enough down the truth table! I was thinking the same as you. Since the 3 input XOR is defined as {A XOR B XOR C}, it makes logical sense, but not common sense.

 

[ljcox]

Ron, I don't think it even makes logical sense. It is simply the truth table of two 2 input XOR gates connected as a 3 input system.

A true XOR should give an active output when one and only one input is active.

The attachment shows 2 of many possible realisations of a 3 input XOR.

 

[Roff]

(A xor B xor C) performs the sum function for a full adder (2 bits plus carry in), so it is useful, but I agree it isn't really a 3-input XOR.

 

[ljcox]

(A xor B xor C) performs the sum function for a full adder (2 bits plus carry in), so it is useful, but I agree it isn't really a 3-input XOR.

Agreed. I had not thought of the full adder.

 

[Roff]

Full adder.
Hungry adder.

 

[ljcox]

In Aus we have the Death Adder. Aptly named.
**broken link removed**

 

[Pommie]

Wouldn't the output of a true 3 input XOR gate only go high when all inputs are exclusive, ie all different. That would be a 1, a 0 and a something else input.

Mike.

 

[Roff]

Wouldn't the output of a true 3 input XOR gate only go high when all inputs are exclusive, ie all different. That would be a 1, a 0 and a something else input.

Mike.

Interesting point, but of course it doesn't work in the binary number system.
I was thinking that exclusive OR is the 'opposite' of inclusive OR. Inclusive OR is where the output is true if one or more inputs is true. Exclusive OR would then be true if one and only one input is true (one input is true, to the exclusion of all others).

 

[dknguyen]

I don't think there is such a thing unless it's nested.

 

[ljcox]

I don't think there is such a thing unless it's nested.

What do you mean by "nested"

 

[AllVol]

In Aus we have the Death Adder. Aptly named.
**broken link removed**

Any udders?