Lesson 6
The Octal System
From eight to ten
Page 216
You are correct. Since 7 is the largest single numeral in the octal system, the number following
178 must be
208 . We can always check this by expanding the octal numbers and converting to decimal:
178
= 1( 81 ) + 7( 80 ) = 1( 8) + 7( 1) = 1510 ;
208
= 2( 81 ) + 0( 80 ) = 2( 8) + 0( 1) = 1610 .
So the octal numbers 178 and 208 correspond to the decimal numbers 1510 and 1610 respectively.
Now we can count in octal as follows:
08 , 18 , ⋯, 78 ,
108 , 118 , ⋯, 178 ,
208 , 218 , ⋯,
308 , ⋯,
408 , ⋯,
508 , ⋯,
608 , ⋯,
708 , ⋯, 778 , ⋯,
where the dots stand for numbers that we aren’t taking the space to write, since you can see how to fill in the blanks for yourself.
How shall we get the next number beyond 778 in the octal system?
In other words, what is 778 + 18 ?
Answer to Self-Test Question 7, Lesson 6 :
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