How do you multiply two octal numbers together?

Answer 1

Base 8 multiplication ( or any other for that matter) uses the same idea as what you are used to in base 10. Let us look at 4x3 in base 10, we know this is 12
4 in octal is 4 in base 10 and 3 in octal is 3 in decimal. But the number 12 means 2 ones and 1 ten. In octal, base 8, we have the digits as powers of 8. So the 1 correspond to 80 and we can only have 7 of them, then we get an 8 in the next digit. So 80 is 8 since it is 0 ones and 1 eight.
Now 3x4 is 12 in base 10 so it is one 8 and 4 ones or 14 in octal.


Now lets look at two numbers in octal and multiply them. How about 14 x14 since we just worked with 14. The good thing is we know what the answer should be since 14 x14 in octal is 12x12=144 in decimal. In octal 144 is 220 since it is 0 ones, 2x82 =64 and 2x81=
128+16=144


Now to multiply it in octal without every even thinking about base 10, here is what we do
write the numbers on top of each other as you normally do for multiplication.


14




14


Now multiply 4x4=16 which is 2x81 so we put a 0 in the 1 column and carry a 2 in the 8 or second column.


i.e. Write a 0 and carry the 2 .


Now we have 4x1=4 and add the 2=6
we have 60 as the first number.
Now beneath that we write the next number which we must add to 60 to get the final answer.
We have 1x4=4 so we can leave that and we have 1x1=1 so we have 140. The 0 was there because it was the second row just as we normally do.


Now add 60+ 140 in octal=220 So the answer is 220


The addition is explained below


0+0=4, first digit is 0.
Next 6+4=10 but the 6 and 4 are not ones, they are 8's so we have ten 8's
We can only have seven of them in that column. We can move 1 over into the next column where it become 1x82 or 64 in base 10 now 80-64=16=2x81
When we carry one over we add it to the 1 in 140 so we now have 220.
To review, the 0 came from 0+0
the 2 came from the 2x8=16 and the first two came from carrying over 1 and adding it to the 1 in 140


Sorry if that was too much detail, but it is a little hard at first. Gets much easier as you do it more. Most brains are programed to base 10 so octal is foreign.