Propositional Logic: Logic Gates Intermediate Warmup

Logic Level 1

The setup above works like a XOR gate (the output will be 1 if exactly one of the inputs is 1). However, the gate marked by a blue box is missing. What is the gate?

OR AND

2 solutions

Pop Wong
Aug 1, 2020

The first one (triangle o) is NOT gate
The second one is AND gate

$(A,B)$	$\bar A$	$\bar B$	$\bar A$ AND $B$	$\bar B$ AND $A$	Input for blue box (up, down)
$(0,0)$	1	1	1 AND 0 = 0	1 AND 0 = 0	$(0, 0)$
$(1,1)$	0	0	0 AND 1 = 0	0 AND 1 = 0	$(0, 0)$
$(1,0)$	0	1	0 AND 0 = 0	1 AND 1 = 1	$(0, 1)$
$(0,1)$	1	0	1 AND 1 = 1	0 AND 0 = 0	$(1, 0)$

so we need an OR gate

Brilliant Mathematics Staff
Aug 1, 2020

You can confirm that the output will be 1 if and only if A = 1 and B = 0, or A = 0 and B = 1.

Propositional Logic: Logic Gates Intermediate Warmup

2 solutions

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