OCTAL ARITHMETIC

OCTAL ARITHMETIC :

(1). Octal Addition:

---> If the sum is less than 8, the addition of two octal digits is same as the equivalent sum.

---> If the sum is greater than or equal to 8, then 8 must be subtracted from the sum to obtain the sum and carry of '1' is produced.

Ex(1):  Add (23)₈ and (67)₈

Sol:       

Column-1: here, 3+7=10,  i.e 10>8, so 8 must be subtracted from 10.

10-8=2 and carry 1 produced.

Column-2: here, 1+2+6=9, i.e 9>8, so 8 must be subtracted from 9

9-8=1 and carry 1 is produced.

Column-3: here, we take the carry also.

Ex(2):  Add (456)₈ and (123)₈

Sol:       

Column-1: here, 6+3=9,  i.e 9>8, so 8 must be subtracted from 9.

9-8=1 and carry 1 produced.

Column-2: here, 1+5+2=8, i.e 8=8, so 8 must be subtracted from 8

8-8=0 and carry 1 is produced.

Column-3: here, 1+4+1=6, i.e 6<8. So, we have to take the same equivalent sum, i.e ‘6’.

(2). Octal Subtraction:

 The subtraction of octal numbers follows the same rules as the subtraction of numbers in any other number system. The only variation is in borrowed number. In the decimal system, you borrow a group of 10₁₀. In the binary system, you borrow a group of 2₁₀. In the octal system you borrow a group of 8₁₀.

Ex (1):