Maximum and minimum values of 7s complement in base 7

[nautolian]

Homework Statement

What are the maximum and minimum values that can be represented using a 7s complement representation in base 7, using a 5 digit number?

Homework Equations

The Attempt at a Solution

Would you divide the numbers so that any number starting with an odd digit is negative and any number starting with an even digit is positive? I actually have no idea how to do this. Would you start with 77777 as the lowest number? and then the highest would be 67777? Thanks in advance for the help

 

[jedishrfu]

use binary as an example and then abstract to base 7

in java for example the min value 2^-31 and the max value is 2^31 -1

http://docs.oracle.com/javase/1.4.2/docs/api/java/lang/Integer.html

 

[nautolian]

In terms of seven's complement though, how would that work.

So for a 5 digit binary number, the highest value would be 01111 (15), and the lowest would be 10001(-15), right? So for seven's complement would you still say odd numbers are negative and evens are positive? So would you add 6 instead of one at the end for 7's complement vs. two's complement? Thanks!

 

[rcgldr]

So for a 5 digit binary number, the highest value would be 01111 (15), and the lowest would be 10001(-15)

For a 5 digit 1's complent number, the lowest value is 10000 (-15), and the highest is 01111 (+15). Note that 11111 is "negative zero" and 00000 is "postive zero".

 

[nautolian]

Don't you have to add 1 at the end for the negative and isn't that two's complement? So how would it work for 7's complement in base 7?

 

[rcgldr]

So how would it work for 7's complement in base 7?

I'm a bit confused by the original post. If each digit ranges from 0 to 7, isn't that a base 8 number? If so, then is the problem statement asking about 7's complement for a base 8 number, which would be similar to 1's complement for a base 2 number? If not, shouldn't each digit for a base 7 number range from 0 to 6, in which case 7's complement for a base 7 number would be similar to 2's complement for a base 2 number?

 

[nautolian]

Sorry, yes, I messed up on that. So it is base 7 with 7s complement. ie, numbers from 0-6.