## Class #6 - Radix Number Representation & Binary Arithmetic.

SCO - Tannenbaum - Appendix A.

### Thought Questions

• The book states that the associative law does not hold for finite precision numbers. Surely, we've all used the associative law in our computer programs at one time or another. So under what conditionions does the associative law hold for our computers? Under what conditions does it not hold?

• Why is excess 2^(m-1) the same as 2's complement with the sign bit reversed?

• Why would two representations of 0, as in signed magnitude or 1's complement, be a problem?

• What is the one negative number in 2's complement that does not have positive counterpart? If we have 8 bit numbers what is the value of this unique number?

• Why is it not possible for overflow to occur if the addend and augend have opposite signs?

• Why is it that overflow can be detected simply by checking to see if the carry in to the last bit differs from the carry out of the last bit?

### Homework Assignment

Due 2/13/96
1. Write the following base 10 numbers in base 2, base 8 and base 16.

1. 22
2. 100
3. 438

### Programming Project

Project 3: Base Conversion and Data Representation
In project 3 you will be writing functions that convert between base2 and base10 numbers. While our simulated computer will not use these functions in their hardware it will make it easier for us to interact with the comptuter. You will also get practice using the BitData class which will be the primary means for passing information between the components of our computer (It will be the wires between our components.)

These pages designed and maintained by Grant Braught
Braught@Dickinson.edu