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UNDERSTAND BOOLEAN LOGIC: FALSE IS ZERO; AND IS *,OR IS + AND EVERYTHING ELSE IS TRUE
UNDERSTAND BOOLEAN LOGIC: FALSE IS ZERO; AND
IS *,OR IS + AND EVERYTHING ELSE IS TRUE
Challenge: You want to become a guru at Excel formulas. To master conditional
computing formulas, you need to understand Boolean logic facts.
Background: For a brief time, I was planning on being an electrical engineer.
While most of the Notre Dame electrical engineering curriculum and I did not
get along, my favorite class was logic design. I learned how to reduce many
decisions down to a series of wires, electricity, and tiny chips that could perform
AND , OR , and NAND operations. I learned how to use Karnaugh maps to reduce
a circuit down to the minimal number of chips. It was fascinating stuff, and it
translates amazingly well to writing criteria in Excel.
With integrated circuits, a circuit is either on or off. On means TRUE , or 1 .
Off means FALSE , or 0 . The table on the left is the truth table for a simple
AND operation. While one approach is to memorize these rules, you can also
convert a problem to a simple mathematical calculation, as in the table on the
right, which converts TRUE to 1 , converts FALSE to 0 , and multiplies the two
values. Notice that the results in A and B in the left table are equivalent to the
results in A*B in the right table.
Boolean Values
Digital Values
Condition
A
Condition
B
A and B
Condition A
Condition B
A*B
FALSE
FALSE
FALSE
0
0
0
FALSE
TRUE
FALSE
0
1
0
TRUE
TRUE
TRUE
1
1
1
TRUE
FALSE
FALSE
1
0
0
With integrated circuits, an OR gate accepts two or more incoming wires. If any
of the incoming wires are on, the output wire is on. Again, you can memorize
the facts in the table on the left below, or you can simply change the TRUE to
1 , the FALSE to 0 , and the OR sign to a plus sign, as in the table on the right. If
the result is 1 or greater, the entire problem is TRUE .
 
 
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