Bit Math - Qeewiki

8/12/2019 Bit Math - Qeewiki

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5/20/2014 C BIT MATH - QEEWiki

https://sites.google.com/site/qeewiki/books/avr-guide/c-bit-math

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My Books > AVR GUIDE>

C BIT MATH

BIT OPERANDS:

The most confusing part of micro controller programming is the fact t hat we have to manipulate data at abit level. While that may seem scary at first it becomes second nature over time. The problem itself is that

there is no really good examples of how this works .... hopefully this chapter will change that.

Most of the time we work with 8 bit data within the AVR (with the exception of the 10 bit ADC).

Understanding bit math gives us a very powerful tool that reduces a lot of manual work.

So, were do shall we begin? How about the Bit shift function.

BIT SHIFT FUNCTIONS ( >)

The bit shift function does just what it says it does, it shifts the data over to the left or over to the right

by one bit. The Bit Shift Funct ion is the most used bit math function when dealing with the AVR.

So lets see this in action in mathematical format. Please note that I will put a space every 4th charact er

to make the numbers easy to read, so 00011000 will read as 0001 1000.

Bit shift left:

(0000 0001 3) = 0000 0010

(1000 0000 >> 0) = 1000 0000

(0000 0001 >> 1) = 0000 0000

Did I do something strange again? in the 3rd example perhaps? nothing moved did it, because as you can

see, the byte was shifted by 0 spaces. But I bet you noticed that the bit in the last example fell of the ....

well beginning of the world this t ime.

Bit Shifts in C:

So now that we have seen a bit of bit shifting in the mathematical model lets take a look at it in code.

i = 1; // i = 0000 0001i = i > 2; // i is now = 0000 0001

See its not as hard as it may seem. However, if you don't understand the theory so far please go back

and re-read this tutorial or post a question, the following theory will build upon this.

There is one final thing to note about bit shifts, they could be used to multiply or divide any number by

any power of 2 (ie 2, 4, 8, 16, 32 ... etc). Lets see this in act ion:

i = 10; // i = 0000 1010i = i >> 1; // i = 0000 0101 = 5 (Shift >> by 1 to divide by 2)i = i


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ow s s use u ecause mu p ca on an v s on use c oc cyc es, w e s ng uses , so s ar

replacing that / and * with a bit shift the next time you need to divide or multiply by 2s 4s and 8s and save

those cycles.

So whats next?

NOT (~)

Not is fairly simple, it basically flips the bit to its opposite.

~0 = 1

~1 = 0

If used in a big register if will change each individual bit to the opposite state.

~ 0000 1111 = 1111 0000

Not in C:

Not is very simple to use, so here it is.

i = 0b10101010;i = ~i; // i is now 01010101

i = 0b11111111;

i = ~i; // i is now 0

AND ( & )

Mathematically and is fairly easy, you compare 2 numbers together, and if they are both TRUE(1) then

your answer is TRUE(1). I like to remember this as: If a AND b is TRUE(1) then the answer is TRUE(1).

0 & 0 = 0

0 & 1 = 0

1 & 0 = 0

1 & 1 = 1

On a bit level it looks fairly easy, however, when we expand the length of bits is looks a bit confusing, so

it is sometimes best to rewrite the byte and put them one on top of the other.

15 & 170 = 10

0000 1111 & 1010 1010 = 0000 1010

0000 1111

& 1010 1010

----------

0000 1010

153 & 170 = 136

1001 1001 & 1010 1010 = 1000 1000

1001 1001

& 1010 1010

----------

1000 1000

6 & 11 = 2

0000 0110 & 0000 1011 = 0000 0010

0000 0110

& 0000 1011 ----------

0000 0010

And in C:

As before this function is fairly simple when you see it in C:i = 6;i = i & 11; // 6 & 11 therefore i = 2

// see last math example above for details

Now, here is where things get a bit confusing, in micro controller programming you will often see the above

code being abbreviated by using &=


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i = 153;i = i & 170; // same as i = i & 170 or i = 153 & 170 // see second last math example above for details

OR and XOR ( | and ^ )

This might be a bit confusing, there are 2 types of OR funct ions, the INCLUSIVE OR ( | ) and the

EXCLUSIVE OR ( ^ ).

OR (INCLUSIVE):

The Inclusive OR is always referred to simply as OR.

The OR funct ion chec ks to see if ether bit is a 1 so basically your asking is variable a OR b true, and

include both true (get it include, inclusive? that's how I always remember it)

0 | 0 = 0

0 | 1 = 1

1 | 0 = 1

1 | 1 = 1

So lets see this in action using a 8 bit number. Once again, I will re-arrange the register one on-top of

the other to make it easier to see what is happening.

15 | 170 = 175

0000 1111 | 1010 1010 = 1010 1111

0000 1111

| 1010 1010

----------

1010 1111

153 | 170 = 187

1001 1001 | 1010 1010 = 1011 1011

1001 1001

| 1010 1010

----------

1011 1011

6 | 11 = 15

0000 0110 | 0000 1011 = 0000 1111

0000 0110

| 0000 1011

----------

0000 1111

OR in C:

So without delay here is what OR looks like in C. As always I use the same numbers in my C code as I do

in my mathematical model above.

i = 15 | 170; // i is now equal to 175 (see above example for the math)

i = 6; // lets set i to 6 for our next examplei = i | 11; // i is now 15 (see above for the math)

XOR:

XOR is the same as OR but it excludes both true values, in other words its only true if both values are

different.

0 ^ 0 = 0

0 ^ 1 = 1

1 ^ 0 = 1

1 ^ 1 = 0

Without delays, lets see the mathematical model once again.

15 ^ 170 = 165

0000 1111 ^ 1010 1010 = 1010 1010

0000 1111

^ 1010 1010

----------

1010 0101

153 ^ 170 = 51

1001 1001

^


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1001 1001 ^ 1010 1010 = 0011 0011

----------

0011 0011

6 ^ 11 = 13

0000 0110 ^ 0000 1011 = 0000 1101

0000 0110

^ 0000 1011

----------

0000 1101

XOR in C:

And for the final time here is what the XOR logic looks like in C.

i = 15 ^ 170; // i now equals 165

i = 6; //sets set i to 6 for our next examplei = i ^ 11; // i now equals 13 (see above)

Well, that's all, our next chapter will cover advance Bit math funct ions, which in lamest terms covers how

to use multiple functions together in order to achieve common AVR tasks such as setting a single pit in a

register.

I hope that I was able to shine some light on a difficult topic. This was the topic that gave me the most

amount of problems when I started out with micro controllers.

And now I'm off to watch cartoons!!!!

Cheers

Q

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Bit Math - Qeewiki