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Number base addition/subtraction

Hi,

I've started doing Computer System Architecture as a unit and I was set to work out how to do addition and subtraction with different number bases. I'm starting to understand addition but subtraction is like jargon to me. I never did Computer Science at GCSE and I'm doing the BTEC IT qualification, so must stuff has been IT related like spreadsheets, databases, business management until I came to this.

I'm managing to add 7 and 3 with bases of 8 and get 12, which is correct. But I was set a question to subtract 22 and 18 with bases of 16 and it's going over my head. I did the working out with the base of 10 which is obviously 4 but it's hard to do this and some extra guidance on how to do the working out would be extremely helpful and appreciated.

Thanks.

Reply 1

winterscoming

Firstly - forget everything you've learned about subtraction since your primary school maths teacher taught you the basics and go back to those fundamental methods using base-10

e.g. To subtract the number 3891 from 7419

Firstly, remember your columns in base-10 are 1, 10, 100 and 1000 and split each significant figure for each number into a separate column with the multiplier for that column. i.e.:



7419 = 7x1000 + 4x100 + 1x10 + 9x1
3891 = 3x1000 + 8x100 + 9x10 + 2x1

Then subtract each column individually, starting from the right-hand-side (the 1s column), and carrying over to the next column if necessary



:
   9x1 -    1x1 -           =    8x1
  1x10 -   9x10 -           =   2x10 carry -1
 4x100 -  8x100 -  1x100(c) =  5x100 carry -1
7x1000 - 3x1000 - 1x1000(c) = 3x1000

Lastly add those together: 3x1000 + 5x100 + 2x10 + 8x1 = 3528

With Base-8 your columns are 1, 8, 64, 512, etc.
With Base-4 your columns are 1, 4, 16, 64, etc.
With Base-5 your columns are 1, 5, 25, 125, etc.
With Base-16 your columns are 1, 16, 256, 4096, etc.

The method is exactly the same regardless of the base. Each time you carry, you need to put a -1 in the next column along towards the left.

(edited 5 years ago)

Reply 2

Phildjm

Original post by winterscoming

Firstly - forget everything you've learned about subtraction since your primary school maths teacher taught you the basics and go back to those fundamental methods using base-10

e.g. To subtract the number 3892 from 7419

Firstly, remember your columns in base-10 are 1, 10, 100 and 1000 and split each significant figure for each number into a separate column with the multiplier for that column. i.e.:


7419 = 7x1000 + 4x100 + 1x10 + 9x1
3891 = 3x1000 + 8x100 + 9x10 + 2x1

Then subtract each column individually, starting from the right-hand-side (the 1s column), and carrying over to the next column if necessary


:
   9x1 -    1x1 -           =    8x1
  1x10 -   9x10 -           =   2x10 carry -1
 4x100 -  8x100 -  1x100(c) =  5x100 carry -1
7x1000 - 3x1000 - 1x1000(c) = 3x1000