I searched for clear explanation with some example close to real life.
What is bit manipulation?
Why we need to use bit manipulation?
We can use bit manipulation in image processing as far as I know. Can anyone show me a simple problem which can be solved using bit manipulation?
I read about bit manipulation from some link:
Link 1
Link 2
In Link 2 Data compression is done using bit packing. Are there any difference between bit manipulation and bit packing?
It will be appreciable If anyone explain me with very simple example which have resemble to real life problem.
What is bit manipulation?
Bit manipulation usually refers to changing data using bit operators.
I think Wikipedia expains it good enough so I won't write another article.
https://en.wikipedia.org/wiki/Bit_manipulation
Bit manipulation is the act of algorithmically manipulating bits or
other pieces of data shorter than a word. Computer programming tasks
that require bit manipulation include low-level device control, error
detection and correction algorithms, data compression, encryption
algorithms, and optimization. For most other tasks, modern programming
languages allow the programmer to work directly with abstractions
instead of bits that represent those abstractions. Source code that
does bit manipulation makes use of the bitwise operations: AND, OR,
XOR, NOT, and possibly other operations analogous to the boolean
operators; there are also bit shifts and operations to count ones and
zeros, find high and low one or zero, set, reset and test bits,
extract and insert fields, mask and zero fields, gather and scatter
bits to and from specified bit positions or fields. Integer arithmetic
operators can also effect bit-operations in conjunction with the other
operators.
Bit manipulation, in some cases, can obviate or reduce the need to
loop over a data structure and can give many-fold speed ups, as bit
manipulations are processed in parallel.
Why we need to use bit manipulation?
Because it is fast and often we don't have another choice. For example in microcontrollers, pretty much everything is controlled by manipulating the bits of 8 bit registers. So an output would go high if you set a certain bit 1.
Bit packing is a compression technique that tries to minimize the number of bits necessary to represent a number. While you'll use bit operators to implement it, it is not the same as "bit-manipulation". It's just one of many many use cases for bit-manipulation.
Can anyone show me a simple problem which can be solved using bit manipulation?
Let's say you have a rgb touple rgb = 0xa1fc03 and you want to make the green channel 0.
rgb_without_green = rgb & 0xFF00FF
We've bitwise ANDed the value with 0xFF00FF.
Now rgb is 0xa10003.
Basically any operation boils down to bit manipulation. For most of them you just have convenient solutions. Say instead of 0x00000011 << 0x0000101 you write 3 * 32
Or have a look at this where the addition of two integers is implemented using bit operations. Add two integers using only bitwise operators?
Edit due to comment
How bitwise AND operation between 0xa1fc03 and 0xFF00FF gives 0xa10003
? Just I need to see how to do this calculation
Bitwise AND means that you AND all the bits of both numbers.
1 AND 1 -> 1
0 AND 1 -> 0
1 AND 0 -> 0
0 AND 0 -> 0
So
0xa1fc03 -> 0b101000011111110000000011
0xff00ff -> 0b111111110000000011111111
AND -> 0b101000010000000000000011
0b101000010000000000000011 -> 0xa10003
With a bit more expierience you know that 0xFF is 0b11111111 so you instantly know that 0xa1fc03 AND 0xff00ff is 0xa1003 becaue you keep everything that is masked with FF and set everything 0 that is masked with 00.
There are countless resources available. You should not have to ask me how to bitwise AND two numbers. Please do your own research.
I am busy designing a new barcode symbology for real-life applications. It uses a checksum value, which is computed on slices of k bits of large numbers. Hence intense bit manipulation.
Looking at this question on Quora HERE ("Are data stored in registers and memory in hex or binary?"), I think the top answer is saying that data persistence is achieved through physical properties of hardware and is not directly relatable to either binary or hex.
I've always thought of computers as 'binary', but have just realized that that only applies to the usage of components (magnetic up/down or an on/off transistor) and not necessarily the organisation of, for example, memory contents.
i.e. you could, theoretically, create an abstraction in memory that used 'binary components' but that wasn't binary, like this:
100000110001010001100
100001001001010010010
111101111101010100001
100101000001010010010
100100111001010101100
And then recognize that as the (badly-drawn) image of 'hello', rather than the ASCII encoding of 'hello'.
An answer on SO (What's the difference between a word and byte?) mentions that processors can handle 'words', i.e. several bytes at a time, so while information representation has to be binary I don't see why information processing has to be.
Can computers do arithmetic on hex directly? In this case, would the internal representation of information in memory/registers be in binary or hex?
Perhaps "digital computer" would be a good starting term and then from there "binary digit" ("bit"). Electronically, the terms for the values are sometimes "high" and "low". You are right, everything after that depends on the operation. Most of the time, groups of bits are operated on together. Commonly groups are 1, 8, 16, 32 and 64 bits. The meaning of the bits depends on the program but some operations go hand-in-hand with some level of meaning.
When the meaning of a group of bits is not known or important, humans like to be able to decern the value of each bit. Binary could be used but more than 8 bits is hard to read. Although it is rare to operate on groups of 4 bits, hexadecimal is much more readable and is generally used regardless of the number of bits. Sometimes octal is used but that's based on contexts where there is some meaning to a subgrouping of the 3 bits or an avoidance of digits beyond 9.
Integers can be stored in two's complement format and often CPUs have instructions for such integers. Once such operation is negation. For a group of 8 bits, it would map 1 to -1,… 127 to -127, and -1 to 1, … -127 to 127, and 0 to 0 and -128 to -128. Decimal is likely the most valuable to humans here, not base 256, base 2 or base 16. In unsigned hexadecimal, that would be 01 to FF, …, 00 to 00, 80 to 80.
For an intro to how a CPU might do integer addition on a group of bits, see adder circuits.
Other number formats include IEEE-754 floating point and binary-coded decimal.
I think you understand that digital circuits are binary. So, based on the above, yes, operations do operate on a higher conceptual level despite the actual storage.
I'm working on some 65802 code (don't ask :P) and I need to separate a 16-bit value into two 8-bit bytes to store it in memory. How would I go about this?
EDIT:
Also, how would I take two similar bytes and combine them into one 16-bit value?
EDIT:
To clarify, many of the solutions available on the internet are not possible with the programming language I'm using (a version of MS-BASIC). I can't take modulo, and I can't left or rightshift. I've figured out that I can put the two bytes together by multiplying the high byte by 256 and adding it to the low byte, but how would I reverse the process?
Why is the smallest value that can be stored a Byte(8bit) & not a Bit(1bit) in memory?
Even booleans are stored as Bytes. Will we ever bump the smallest number to 32 or 64bits like register's on the CPU?
EDIT: To clarify as many answers seemed confused about the nature of questing. This question is about why isn't a byte 7-bit, 1-bit, 32-bit, etc (not why lower bit primitives must fit within the hardware's byte at min). Is the 8-bit byte simply historical as some hardware has 10-bit bytes for example. Or is there a mathematical reason 8-bit is ideal vs say 10-bit for general processing?
The hardware is built to read data in blocks (bytes, later words and dwords). This provides greater efficiency, than accessing individual bits, and also offers more addressing range. So most data is aligned to at least byte boundary. There exist encodings that operate with bit sequences, rather than bytes, but they are quite rare.
Nowadays the data is most often aligned to dword (32-bits) boundary anyway. Moreover, some hardware (ARM, for example), can't access misaligned multibyte variables, i.e. 16-bit word can't "cross" dword boundary - exception will be thrown.
Because computers address memory at the byte level, so anything smaller than a byte is not addressable.
The underlying methods of processor access are limited to the size of the smallest usable register. On most architectures, that size is 8 bits. You can use smaller portions of these; for instance, C has the bitfield feature in structs that will allow combining fields that only need to be certain bit lengths. Access will still require that the whole byte be read.
Some older exotic architectures actually did have different a "word size." In these machines, 10 bits might be the common size.
Lastly, processors are almost always backwards compatible. Intel, for instance, has maintained complete instruction compatibility from the 386 on up. If you take a program compiled for the 386, it will still run on an i7 processor. Changing the word size would break compatibility. So while it is possible, no manufacturer will ever do it.
Assume that we have native language that consist of 2 character such as a , b
to distinguish two characters we need at least 1 bit for example 0 to represent char a and 1 to represent char b
so that if we count number of characters and special characters and symbols, there are 128 character and to distinguish one character from another, you need log2(128) = 7 bit and 8th bit for transmission
How seriously do developers think about using a 16bit integer when writing code? I've been using 32bit integers ever since I've been programming and I don't really think about using 16bit.
Its so easy to declare a 32bit int because its the default for most languages.
Whats the upside of using a 16bit integer apart from a little memory saved?
Now that we have cars, we don't walk or ride horses as much, but we still do walk and ride horses.
There is less need to use shorts these days. In a lot of situations the cost of disk space and availability of RAM mean that we no longer need to squeeze every last bit of storage out of computers as we did 20 years ago, so we can sacrifice a bit of storage efficiency in order to save on development/maintenance costs.
However, where large amounts of data are used, or we are working with systems with small memories (e.g. embedded controllers) or when we are transmitting data over networks, using 32 or 64 bits to represent a 16-bit value is just a waste of memory/bandwidth. It doesn't matter how much memory you have, wasting half or three quarters of it would just be stupid.
APIs/interfaces (e.g. TCP/IP port numbers) and algorithms that require manipulation (e.g. rotation) of 16-bit values.
I was interested in the relative performance so I wrote this small test program to perform a very simple test of the speed of allocating, using, and freeing a significant amount of data in both int and short format.
I run the tests several times in case caching and so on are affected.
#include <iostream>
#include <windows.h>
using namespace std;
const int DATASIZE = 1000000;
template <typename DataType>
long long testCount()
{
long long t1, t2;
QueryPerformanceCounter((LARGE_INTEGER*)&t1);
DataType* data = new DataType[DATASIZE];
for(int i = 0; i < DATASIZE; i++) {
data[i] = 0;
}
delete[] data;
QueryPerformanceCounter((LARGE_INTEGER*)&t2);
return t2-t1;
}
int main()
{
cout << "Test using short : " << testCount<short>() << " ticks.\n";
cout << "Test using int : " << testCount<int>() << " ticks.\n";
cout << "Test using short : " << testCount<short>() << " ticks.\n";
cout << "Test using int : " << testCount<int>() << " ticks.\n";
cout << "Test using short : " << testCount<short>() << " ticks.\n";
cout << "Test using int : " << testCount<int>() << " ticks.\n";
cout << "Test using short : " << testCount<short>() << " ticks.\n";
}
and here are the results on my system (64 bit quad core system running windows7 64 bit, but the program is a 32 bit program built using VC++ express 2010 beta in release mode)
Test using short : 3672 ticks.
Test using int : 7903 ticks.
Test using short : 4321 ticks.
Test using int : 7936 ticks.
Test using short : 3697 ticks.
Test using int : 7701 ticks.
Test using short : 4222 ticks.
This seems to show that there are significant performance advantages at least in some cases to using short instead of int when there is a large amount of data. I realise that this is far from being a comprehensive test, but it's some evidence that not only do they use less space but they can be faster to process too at least in some applications.
when there is memory constraints short can help u lot. for e.g. while coding for embedded systems, u need to consider the memory.
16-bit values are still in great demand (though unsigned would do - don't really need signed).
For example,
16 bit Unicode - UTF-16/UCS-2.
16 bit graphics - especially for embedded devices.
16 bit checksums - for UDP headers and similar.
16 Bit devices - e.g. many norflash devices are 16 bit.
You might need to wrap at 65535.
You might need to work with a message sent from a device which includes fields which are 16 bit. Using 32 bit integers in this case would cause you to be accessing bits at the wrong offset in the message.
You might be working on an embedded 16 bit micro, or an embedded 8 bit micro. Hint: not all processors are x86, 32 bit.
This is really important in database development, because sometimes people are using a lot more space than is really needed (e.g. using int when small would have been sufficient). When you have tables with millions of rows this can be important factor in e.g. database size and queries. I would recommend people using always the appropriate datatype for columns.
I also try to use the correct datatype for other development, I know it can be a pain dealing with long and small (pretty convenient to have everyting int) but I think it pays off in the end, for example when serializing objects.
you ask: Any good reason to keep them around?
Since you say 'language-agnostic' the answer is a 'certainly yes'.
The computer CPU still works with bytes, words, full registers and whatnot, no matter how much these 'data types' are abstracted by some programming languages. There will always be situations where the code needs to 'touch the metal'.
It's hardly a little memory saved [read: 50%] when you allocate memory for a large number of numeric values. Common uses are:
COM and external device interop
Reducing memory consumption for large arrays where each number will never exceed a couple thousands in magnitude
Unique hashes for pairs of objects, where no more than ~65K objects are needed (hash values can only be 32-bit ints, but note that hash table types must transform the value for internal representations so collisions are still likely, but equality can be based on exact hash matches)
Speed up algorithms that rely on structs (smaller sized value types translates to increased performance when they are copied around in memory)
In large arrays, "little memory saved" could instead be "much memory saved".
The use of 16 bit integers is primarily for when you need to encode things for transmission over a network, for saving on hard disk, etc. without using up any more space than necessary. It might also occasionally be useful to save memory if you have a very large array of integers, or a lot of objects that contain integers.
Use of 16 bit integers without there being a good memory saving reason is pretty pointless. And 16 bit local variables are most often silently implemented with 32 or 64 bit integers anyway.
you have probably been using the 16 bit datatype more often than you knew. The char datatype in both C# and Java are 16 bit. Unicode is typically stored in a 16bit datatype.
The question should really be why we need a 16-bit primitive data type, and the answer would be that there is an awful lot of data out there which is naturally represented in 16 bits. One ubiquitous example is audio, e.g. CD audio is represented as streams of 16 bit signed integers.
16 bits is still plenty big enough to hold pixel channel values (e.g. R, G, or B). Most pixels only use 8 bits to store a channel, but Photoshop has a 16-bit mode that professionals use.
In other words, a pixel might be defined as struct Pixel16 { short R, G, B, A; } or an image might be defined as separate channels of struct Channel16 { short channel[]; }
I think most people use the default int on their platform. However there are times when you have to communicate with older systems or libraries that are expecting 16 bit or even eight bit integers (thank god we don't have to worry about 12 bit integers any more). This is especially true for databases. Also, if you're doing bit masking or bit shifting, you might have an algorithm that specifies the length of the integer. By default, and on platforms where memory is cheap, you should probably use integers sized to your processor.
Those 2 bytes add up. Your data types eventually become part of array or databases or messages, they go into data files. It adds up to a lot of wasted space and on embedded systems it can make a huge difference.
When we do peer review of our code at work, if something is sized incorrectly, it will be written as a discrepancy and must be corrected. If we find something that has a range of 1-1000 using an int32_t, it has to be corrected. The range must also be documented in a comment. Our department does not allow use of int, long, etc, we must use int32_t, int16_t, uint16_t, etc. so that the expected size is documented.
uint16_t conicAngle; // angle in tenths of a degree (range 0..3599)
or in Ada:
type Amplitude is range 0 .. 255; // signal amplitude from FPGA
Get in the habit of using what you need and no more and documenting what you need (if the language doesn't support it).
We are currently in the process of fixing a performance problem by resizing the data types in several messages, they have 32 bit fields that could be 8 or 16 bit. By resizing them appropriately we can reduce the message rate in half and improve our data throughput to meet the requirements.
Once upon a time, in the land of Earth, there existed devices called computers.
In the early days following the invention of "computers," there was limited storage in memory for fancy things like numbers and strings.
Billy, a programmer, was encouraged by the evil Wizard (his boss) to use the least amount of memory that he could!
Then one day, memory sizes got large enough that everyone could use 32-bit numbers if they wanted!
I could continue on, but all the other obvious things were already covered.