Fundamentals of Data Representation: Status register

From Wikibooks, open books for an open world
Jump to: navigation, search

UNIT 1 - ⇑ Fundamentals of Data Representation ⇑

← Two's complement Status register Information coding schemes →

Maths in a processor is normally performed using set numbers of bits. For example where you add 8 bits to 8 bits. This will often cause no problems at all:

 00110011 (51)
+00001010 (10)
 --------
 00111101 (61)

But what happens if we add the following numbers together:

 01110011 (115)
+01001010 (74)
 --------
 10111101 (189)

This may appear to have gone ok, but we have a problem. If we are dealing with twos complement numbers the answer from adding two positive numbers together is negative!

 01110011 (115)
+01001010 (74)
 --------
 10111101 (-67!)

Overflow[edit]

Let's take a look at another problem example, the problem of overflow

Overflow - When a the result of a calculation is too large to fit into a set number of bits


    1010 (-6)
   +1010 (-6)
    --------
 (1)0100 (+4!)

As you can see in the sum above, we have added two negative numbers together and the result is a positive number.

To deal with the situations mentioned above we use the status register

Status Register - information about process states such as whether a result is zero, positive/negative or resulted in overflow.


The most common flags[edit]

Flag Name Description
Z Zero flag Indicates that the result of an arithmetic or logical operation (or, sometimes, a load) was zero.
C Carry flag Enables numbers larger than a single word (in the examples above 4 or 8 bits) to be added/subtracted by carrying a binary digit from a less significant word to the least significant bit of a more significant word as needed
S / N Sign flag / Negative flag One indicates whether the result was negative whereas the other indicates whether a subtraction or addition has taken place.
O Overflow flag Indicates that the signed result of an operation is too large to fit in the register width using twos complement representation.
P Parity flag Indicates whether the number of set bits of the last result is odd or even.
Status register working

For the sum that we met earlier we will take a look at how the status register can be used to stop the incorrect answer arising:

 01110011 (115)
+01001010 (74)
 --------
 10111101 (-67)

Status register: Z = False | C = False | N = True | O = True | P = Even

Using these flags you can see that the result is negative, if the original sum used only positive values, then we know we have an error.

Looking at the other equation:

    1010 (-6)
   +1010 (-6)
    ----
 (1)0100

Status register: Z = False | C = True | N = False | O = True | P = Odd

Using these flags you can see that the result is positive when the original used two negative numbers. We can also see that overflow occurred.

Exercise: Status register
What is the problem with the result of the following 4 bit sum:
    1011 (-5)
   +1011 (-5)
    ----

Answer :

The result would create overflow, giving an incorrect answer:
    1011 (-5)
   +1011 (-5)
    ----
 (1)0110 (+6)

In the context of calculations what is overflow?

Answer :

When a the result of a calculation is too large to fit into a set number of bits.

What do we need the status register for?

Answer :

The status register holds flags keeping track of the results of sums, this helps us to see when there is an error in a result and correct it accordingly

Name three flags in a status register:

Answer :

Overflow, Carry, Negative, Zero

Show the Status register for the following sum:
    1001 (-7)
   +1001 (-7)
    ----
 (1)0010 (+6)

Answer :

Status register: Z = False | C = True | N = False | O = True | P = Odd