The tutor explains a consequence of octal logic.

Octal logic focuses on numbers in base 8. An octal number has the following form:

p(2⁰)+q(2¹)+r(2²)

which evaluates to

p(1)+q(2)+r(4)

where p,q,r have possible values 0 or 1 (“off” or “on”).

The number 6 is

0(1)+1(2)+1(4): q,r=1

The number 5 is

1(1)+0(2)+1(4): p,r=1

The AND operation puts a 1 only where both inputs already equal 1. From above, we see that for 6 and 5, only r is 1 in both. Since r is the coefficient of 4, we have 6 AND 5 = (1)4 = 4.

Source:

Grimaldi, Ralph P. Discrete and Combinatorial Mathematics. Don Mills: Addison-Wesley, 1994.

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