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Saturday, 5 December 2009
Data representation methods in a computer.
2.2.2.1 ASCII code
ASCII is an acronym of American Standard Code for Information Interchange. This code assigns the letters of the alphabet, decimal digits from 0 to 9 and some additional symbols a binary number of 7 bits, putting the 8th bit in its off state or 0. This way each letter, digit or special character occupies one byte in the computer memory.
We can observe that this method of data representation is very inefficient on the numeric aspect, since in binary format one byte is not enough to represent numbers from 0 to 255, but on the other hand with the ASCII code one byte may represent only one digit. Due to this inefficiency, the ASCII code is mainly used in the memory to represent text.
2.2.2.2 BCD Method
BCD is an acronym of Binary Coded Decimal. In this notation groups of 4 bits are used to represent each decimal digit from 0 to 9. With this method we can represent two digits per byte of information.
Even when this method is much more practical for number representation in the memory compared to the ASCII code, it still less practical than the binary since with the BCD method we can only represent digits from 0 to 99. On the other hand in binary format we can represent all digits from 0 to 255.
This format is mainly used to represent very large numbers in mercantile applications since it facilitates operations avoiding mistakes.
2.2.2.3 Floating point representation
This representation is based on scientific notation, this is, to represent a number in two parts: its base and its exponent.
As an example, the number 1234000, can be represented as 1.123*10^6, in this last notation the exponent indicates to us the number of spaces that the decimal point must be moved to the right to obtain the original result.
In case the exponent was negative, it would be indicating to us the number of spaces that the decimal point must be moved to the left to obtain the original result.
ASCII is an acronym of American Standard Code for Information Interchange. This code assigns the letters of the alphabet, decimal digits from 0 to 9 and some additional symbols a binary number of 7 bits, putting the 8th bit in its off state or 0. This way each letter, digit or special character occupies one byte in the computer memory.
We can observe that this method of data representation is very inefficient on the numeric aspect, since in binary format one byte is not enough to represent numbers from 0 to 255, but on the other hand with the ASCII code one byte may represent only one digit. Due to this inefficiency, the ASCII code is mainly used in the memory to represent text.
2.2.2.2 BCD Method
BCD is an acronym of Binary Coded Decimal. In this notation groups of 4 bits are used to represent each decimal digit from 0 to 9. With this method we can represent two digits per byte of information.
Even when this method is much more practical for number representation in the memory compared to the ASCII code, it still less practical than the binary since with the BCD method we can only represent digits from 0 to 99. On the other hand in binary format we can represent all digits from 0 to 255.
This format is mainly used to represent very large numbers in mercantile applications since it facilitates operations avoiding mistakes.
2.2.2.3 Floating point representation
This representation is based on scientific notation, this is, to represent a number in two parts: its base and its exponent.
As an example, the number 1234000, can be represented as 1.123*10^6, in this last notation the exponent indicates to us the number of spaces that the decimal point must be moved to the right to obtain the original result.
In case the exponent was negative, it would be indicating to us the number of spaces that the decimal point must be moved to the left to obtain the original result.
calculation for haxadecimal and others
2.2.1.1 Information Units
In order for the PC to process information, it is necessary that this information be in special cells called registers. The registers are groups of 8 or 16 flip-flops.
A flip-flop is a device capable of storing two levels of voltage, a low one, regularly 0.5 volts, and another one, commonly of 5 volts. The low level of energy in the flip-flop is interpreted as off or 0, and the high level as on or 1. These states are usually known as bits, which are the smallest information unit in a computer.
A group of 16 bits is known as word; a word can be divided in groups of 8 bits called bytes, and the groups of 4 bits are called nibbles.
2.2.1.2 Numeric systems
The numeric system we use daily is the decimal system, but this system is not convenient for machines since the information is handled codified in the shape of on or off bits; this way of codifying takes us to the necessity of knowing the positional calculation which will allow us to express a number in any base where we need it.
It is possible to represent a determined number in any base through the following formula:
Where n is the position of the digit beginning from right to left and numbering from zero. D is the digit on which we operate and B is the used numeric base.
2.2.1.3 converting binary numbers to decimals
When working with assembly language we come on the necessity of converting numbers from the binary system, which is used by computers, to the decimal
system used by people.
The binary system is based on only two conditions or states, be it on(1) or off(0), thus its base is two.
For the conversion we can use the positional value formula:
For example, if we have the binary number of 10011, we take each digit from right to left and multiply it by the base, elevated to the new position they are:
Binary: 1 1 0 0 1
Decimal: 1*2^0 + 1*2^1 + 0*2^2 + 0*2^3 + 1*2^4
= 1 + 2 + 0 + 0 + 16 = 19 decimal.
The ^ character is used in computation as an exponent symbol and the * character is used to represent multiplication.
2.2.1.4 Converting decimal numbers to binary
There are several methods to convert decimal numbers to binary; only one
will be analyzed here. Naturally a conversion with a scientific calculator is much easier, but one cannot always count with one, so it is convenient to at least know one formula to do it.
The method that will be explained uses the successive division of two, keeping the residue as a binary digit and the result as the next number to divide.
Let us take for example the decimal number of 43.
43/2=21 and its residue is 1
21/2=10 and its residue is 1
10/2=5 and its residue is 0
5/2=2 and its residue is 1
2/2=1 and its residue is 0
1/2=0 and its residue is 1
Building the number from the bottom , we get that the binary result is
101011
2.2.1.5 Hexadecimal system
On the hexadecimal base we have 16 digits which go from 0 to 9 and from the letter A to the F, these letters represent the numbers from 10 to 15. Thus we count 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E, and F.
The conversion between binary and hexadecimal numbers is easy. The first thing done to do a conversion of a binary number to a hexadecimal is to divide it in groups of 4 bits, beginning from the right to the left. In case the last group, the one most to the left, is under 4 bits, the missing places are filled with zeros.
Taking as an example the binary number of 101011, we divide it in 4 bits groups and we are left with:
10;1011
Filling the last group with zeros (the one from the left):
0010;1011
Afterwards we take each group as an independent number and we consider its
decimal value:
0010=2;1011=11
But since we cannot represent this hexadecimal number as 211 because it would be an error, we have to substitute all the values greater than 9 by their respective representation in hexadecimal, with which we obtain:
2BH, where the H represents the hexadecimal base.
In order to convert a hexadecimal number to binary it is only necessary to invert the steps: the first hexadecimal digit is taken and converted to binary, and then the second, and so on.
In order for the PC to process information, it is necessary that this information be in special cells called registers. The registers are groups of 8 or 16 flip-flops.
A flip-flop is a device capable of storing two levels of voltage, a low one, regularly 0.5 volts, and another one, commonly of 5 volts. The low level of energy in the flip-flop is interpreted as off or 0, and the high level as on or 1. These states are usually known as bits, which are the smallest information unit in a computer.
A group of 16 bits is known as word; a word can be divided in groups of 8 bits called bytes, and the groups of 4 bits are called nibbles.
2.2.1.2 Numeric systems
The numeric system we use daily is the decimal system, but this system is not convenient for machines since the information is handled codified in the shape of on or off bits; this way of codifying takes us to the necessity of knowing the positional calculation which will allow us to express a number in any base where we need it.
It is possible to represent a determined number in any base through the following formula:
Where n is the position of the digit beginning from right to left and numbering from zero. D is the digit on which we operate and B is the used numeric base.
2.2.1.3 converting binary numbers to decimals
When working with assembly language we come on the necessity of converting numbers from the binary system, which is used by computers, to the decimal
system used by people.
The binary system is based on only two conditions or states, be it on(1) or off(0), thus its base is two.
For the conversion we can use the positional value formula:
For example, if we have the binary number of 10011, we take each digit from right to left and multiply it by the base, elevated to the new position they are:
Binary: 1 1 0 0 1
Decimal: 1*2^0 + 1*2^1 + 0*2^2 + 0*2^3 + 1*2^4
= 1 + 2 + 0 + 0 + 16 = 19 decimal.
The ^ character is used in computation as an exponent symbol and the * character is used to represent multiplication.
2.2.1.4 Converting decimal numbers to binary
There are several methods to convert decimal numbers to binary; only one
will be analyzed here. Naturally a conversion with a scientific calculator is much easier, but one cannot always count with one, so it is convenient to at least know one formula to do it.
The method that will be explained uses the successive division of two, keeping the residue as a binary digit and the result as the next number to divide.
Let us take for example the decimal number of 43.
43/2=21 and its residue is 1
21/2=10 and its residue is 1
10/2=5 and its residue is 0
5/2=2 and its residue is 1
2/2=1 and its residue is 0
1/2=0 and its residue is 1
Building the number from the bottom , we get that the binary result is
101011
2.2.1.5 Hexadecimal system
On the hexadecimal base we have 16 digits which go from 0 to 9 and from the letter A to the F, these letters represent the numbers from 10 to 15. Thus we count 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E, and F.
The conversion between binary and hexadecimal numbers is easy. The first thing done to do a conversion of a binary number to a hexadecimal is to divide it in groups of 4 bits, beginning from the right to the left. In case the last group, the one most to the left, is under 4 bits, the missing places are filled with zeros.
Taking as an example the binary number of 101011, we divide it in 4 bits groups and we are left with:
10;1011
Filling the last group with zeros (the one from the left):
0010;1011
Afterwards we take each group as an independent number and we consider its
decimal value:
0010=2;1011=11
But since we cannot represent this hexadecimal number as 211 because it would be an error, we have to substitute all the values greater than 9 by their respective representation in hexadecimal, with which we obtain:
2BH, where the H represents the hexadecimal base.
In order to convert a hexadecimal number to binary it is only necessary to invert the steps: the first hexadecimal digit is taken and converted to binary, and then the second, and so on.
Computer is What for assemble?
Computer System.
We call computer system to the complete configuration of a computer, including the peripheral units and the system programming which make it a useful and functional machine for a determined task.
2.1.1 Central Processor.
This part is also known as central processing unit or CPU, which in turn is made by the control unit and the arithmetic and logic unit. Its functions consist in reading and writing the contents of the memory cells, to forward data between memory cells and special registers, and decode and execute the instructions of a program. The processor has a series of memory cells which are used very often and thus, are part of the CPU. These cells are known with the name of registers. A processor may have one or two dozen of these registers. The arithmetic and logic unit of the CPU realizes the operations related with numeric and symbolic calculations. Typically these units only have capacity of performing very elemental operations such as: the addition and subtraction of two whole numbers, whole number multiplication and division, handling of the registers' bits and the comparison of the content of two registers. Personal computers can be classified by what is known as word size, this is, the quantity of bits which the processor can handle at a time.
2.1.2 Central Memory.
It is a group of cells, now being fabricated with semi-conductors, used for general processes, such as the execution of programs and the storage of information for the operations.
Each one of these cells may contain a numeric value and they have the property of being addressable, this is, that they can distinguish one from another by means of a unique number or an address for each cell.
The generic name of these memories is Random Access Memory or RAM. The main disadvantage of this type of memory is that the integrated circuits lose the information they have stored when the electricity flow is interrupted. This was the reason for the creation of memories whose information is not lost when the system is turned off. These memories receive the name of Read Only Memory or ROM.
2.1.3 Input and Output Units.
In order for a computer to be useful to us it is necessary that the processor communicates with the exterior through interfaces which allow the input and output of information from the processor and the memory. Through the use of these communications it is possible to introduce information to be processed and to later visualize the processed data.
Some of the most common input units are keyboards and mice. The most common output units are screens and printers.
2.1.4 Auxiliary Memory Units.
Since the central memory of a computer is costly, and considering today's applications it is also very limited. Thus, the need to create practical and economical information storage systems arises. Besides, the central memory loses its content when the machine is turned off, therefore making it inconvenient for the permanent storage of data.
These and other inconvenience give place for the creation of peripheral units of memory which receive the name of auxiliary or secondary memory. Of these the most common are the tapes and magnetic discs.
The stored information on these magnetic media means receive the name of files. A file is made of a variable number of registers, generally of a fixed size; the registers may contain information or programs.
We call computer system to the complete configuration of a computer, including the peripheral units and the system programming which make it a useful and functional machine for a determined task.
2.1.1 Central Processor.
This part is also known as central processing unit or CPU, which in turn is made by the control unit and the arithmetic and logic unit. Its functions consist in reading and writing the contents of the memory cells, to forward data between memory cells and special registers, and decode and execute the instructions of a program. The processor has a series of memory cells which are used very often and thus, are part of the CPU. These cells are known with the name of registers. A processor may have one or two dozen of these registers. The arithmetic and logic unit of the CPU realizes the operations related with numeric and symbolic calculations. Typically these units only have capacity of performing very elemental operations such as: the addition and subtraction of two whole numbers, whole number multiplication and division, handling of the registers' bits and the comparison of the content of two registers. Personal computers can be classified by what is known as word size, this is, the quantity of bits which the processor can handle at a time.
2.1.2 Central Memory.
It is a group of cells, now being fabricated with semi-conductors, used for general processes, such as the execution of programs and the storage of information for the operations.
Each one of these cells may contain a numeric value and they have the property of being addressable, this is, that they can distinguish one from another by means of a unique number or an address for each cell.
The generic name of these memories is Random Access Memory or RAM. The main disadvantage of this type of memory is that the integrated circuits lose the information they have stored when the electricity flow is interrupted. This was the reason for the creation of memories whose information is not lost when the system is turned off. These memories receive the name of Read Only Memory or ROM.
2.1.3 Input and Output Units.
In order for a computer to be useful to us it is necessary that the processor communicates with the exterior through interfaces which allow the input and output of information from the processor and the memory. Through the use of these communications it is possible to introduce information to be processed and to later visualize the processed data.
Some of the most common input units are keyboards and mice. The most common output units are screens and printers.
2.1.4 Auxiliary Memory Units.
Since the central memory of a computer is costly, and considering today's applications it is also very limited. Thus, the need to create practical and economical information storage systems arises. Besides, the central memory loses its content when the machine is turned off, therefore making it inconvenient for the permanent storage of data.
These and other inconvenience give place for the creation of peripheral units of memory which receive the name of auxiliary or secondary memory. Of these the most common are the tapes and magnetic discs.
The stored information on these magnetic media means receive the name of files. A file is made of a variable number of registers, generally of a fixed size; the registers may contain information or programs.
Introduction of the Assembly
1.1 What's new in the Assembler material
After of one year that we've released the first Assembler material on-line. We've received a lot of e-mail where each people talk about different aspects about this material. We've tried to put these comments and suggestions in this update assembler material. We hope that this new Assembler material release reach to all people that they interest to learn the most important language for IBM PC.
In this new assembler release includes:
A complete chapter about how to use debug program
More example of the assembler material
Each section of this assembler material includes a link file to Free
On-line of Computing by Dennis Howe
Finally, a search engine to look for any topic or item related with this updated material.
1.2 Presentation
The document you are looking at, has the primordial function of introducing you to assembly language programming, and it has been thought for those people who have never worked with this language.
The tutorial is completely focused towards the computers that function with processors of the x86 family of Intel, and considering that the language bases its functioning on the internal resources of the processor, the described examples are not compatible with any other architecture.
The information was structured in units in order to allow easy access to each of the topics and facilitate the following of the tutorial.
In the introductory section some of the elemental concepts regarding computer systems are mentioned, along with the concepts of the assembly language itself, and continues with the tutorial itself.
1.3 Why learn assembler language
The first reason to work with assembler is that it provides the opportunity of knowing more the operation of your PC, which allows the development of software in a more consistent manner.
The second reason is the total control of the PC which you can have with the use of the assembler.
Another reason is that the assembly programs are quicker, smaller, and have
larger capacities than ones created with other languages.
Lastly, the assembler allows an ideal optimization in programs, be it on their size or on their execution.
1.4 We need your opinion
Our goal is offers you easier way to learn yourself assembler language. You send us your comments or suggestions about this 96' edition. Any comment will be welcome.
After of one year that we've released the first Assembler material on-line. We've received a lot of e-mail where each people talk about different aspects about this material. We've tried to put these comments and suggestions in this update assembler material. We hope that this new Assembler material release reach to all people that they interest to learn the most important language for IBM PC.
In this new assembler release includes:
A complete chapter about how to use debug program
More example of the assembler material
Each section of this assembler material includes a link file to Free
On-line of Computing by Dennis Howe
Finally, a search engine to look for any topic or item related with this updated material.
1.2 Presentation
The document you are looking at, has the primordial function of introducing you to assembly language programming, and it has been thought for those people who have never worked with this language.
The tutorial is completely focused towards the computers that function with processors of the x86 family of Intel, and considering that the language bases its functioning on the internal resources of the processor, the described examples are not compatible with any other architecture.
The information was structured in units in order to allow easy access to each of the topics and facilitate the following of the tutorial.
In the introductory section some of the elemental concepts regarding computer systems are mentioned, along with the concepts of the assembly language itself, and continues with the tutorial itself.
1.3 Why learn assembler language
The first reason to work with assembler is that it provides the opportunity of knowing more the operation of your PC, which allows the development of software in a more consistent manner.
The second reason is the total control of the PC which you can have with the use of the assembler.
Another reason is that the assembly programs are quicker, smaller, and have
larger capacities than ones created with other languages.
Lastly, the assembler allows an ideal optimization in programs, be it on their size or on their execution.
1.4 We need your opinion
Our goal is offers you easier way to learn yourself assembler language. You send us your comments or suggestions about this 96' edition. Any comment will be welcome.
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