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Numbers, Characters and Strings. This chapter defines the various data types supported by the compiler. Since the objective of most computer systems is to process data, it is important to understand how data is stored and interpreted by the software.
We define a literal as the direct specification of the number, character, or string. We will discuss the way data are stored on the computer as well as the C syntax for creating the literals. The Imagecraft and Metrowerks compilers recognize three types of literals numeric , character , string. Numbers can be written in three bases decimal , octal , and hexadecimal. Although the programmer can choose to specify numbers in these three bases, once loaded into the computer, the all numbers are stored and processed as unsigned or signed binary.
Although C does not support the binary literals, if you wanted to specify a binary number, you should have no trouble using either the octal or hexadecimal format. Numbers are stored on the computer in binary form. On most computers, the memory is organized into 8-bit bytes. This means each 8-bit byte stored in memory will have a separate address. Precision is the number of distinct or different values. We express precision in alternatives, decimal digits, bytes, or binary bits.
Alternatives are defined as the total number of possibilities. For example, an 8-bit number scheme can represent different numbers. For example, a voltmeter with a range of 0. Let the operation [[ x ]] be the greatest integer of x. For large numbers we use abbreviations, as shown in the following table.
Computer engineers use the same symbols as other scientists, but with slightly different values. If a byte is used to represent an unsigned number, then the value of the number is. There are different unsigned 8-bit numbers. The smallest unsigned 8-bit number is 0 and the largest is Other examples are shown in the following table. The basis of a number system is a subset from which linear combinations of the basis elements can be used to construct the entire set.
For the unsigned 8-bit number system, the basis is. One way for us to convert a decimal number into binary is to use the basis elements. The overall approach is to start with the largest basis element and work towards the smallest. One by one we ask ourselves whether or not we need that basis element to create our number. If we do, then we set the corresponding bit in our binary result and subtract the basis element from our number.
If we do not need it, then we clear the corresponding bit in our binary result. We will work through the algorithm with the example of converting to 8 bit binary. We with the largest basis element in this case and ask whether or not we need to include it to make Since our number is less than , we do not need it so bit 7 is zero.
We go the next largest basis element, 64 and ask do we need it. We do need 64 to generate our , so bit 6 is one and subtract minus 64 to get Next we go the next basis element, 32 and ask do we need it.
Again we do need 32 to generate our 36, so bit 5 is one and we subtract 36 minus 32 to get 4. Continuing along, we need basis element 4 but not 16 8 2 or 1, so bits are respectively. We define an unsigned 8-bit number using the unsigned char format. When a number is stored into an unsigned char it is converted to 8-bit unsigned value. There are also different signed 8 bit numbers. The smallest signed 8-bit number is and the largest is Notice that the same binary pattern of 2 could represent either or It is very important for the software developer to keep track of the number format.
The computer can not determine whether the 8-bit number is signed or unsigned. You, as the programmer, will determine whether the number is signed or unsigned by the specific assembly instructions you select to operate on the number. Some operations like addition, subtraction, and shift left multiply by 2 use the same hardware instructions for both unsigned and signed operations.
On the other hand, multiply, divide, and shift right divide by 2 require separate hardware instruction for unsigned and signed operations. The compiler will automatically choose the proper implementation. It is always good programming practice to have clear understanding of the data type for each number, variable, parameter, etc. For some operations there is a difference between the signed and unsigned numbers while for others it does not matter.
The point is that care must be taken when dealing with a mixture of numbers of different sizes and types. Similar to the unsigned algorithm, we can use the basis to convert a decimal number into signed binary. We will work through the algorithm with the example of converting to 8-bit binary.
We with the largest basis element in this case and decide do we need to include it to make Yes without , we would be unable to add the other basis elements together to get any negative result , so we set bit 7 and subtract the basis element from our value.
Our new value is minus , which is We do not need 64 to generate our 28, so bit6 is zero. We do not need 32 to generate our 28, so bit5 is zero. Continuing along, we need basis elements 8 and 4 but not 2 1, so bits are First we do a logic complement flip all bits to get Then add one to the result to get A third way to convert negative numbers into binary is to first subtract the number from , then convert the unsigned result to binary using the unsigned method.
For example, to find , we subtract minus to get Then we convert to binary resulting in This method works because in 8 bit binary math adding to number does not change the value. We define a signed 8-bit number using the char format. When a number is stored into a char it is converted to 8-bit signed value. A halfword or double byte contains 16 bits. A word contains 32 bits. If a word is used to represent an unsigned number, then the value of the number is.
There are 65, different unsigned bit numbers. The smallest unsigned bit number is 0 and the largest is We define an unsigned bit number using the unsigned short format. When a number is stored into an unsigned short it is converted to bit unsigned value. There are also 65, different signed bit numbers. The smallest signed bit number is and the largest is To improve the quality of our software, we should always specify the precision of our data when defining or accessing the data.
We define a signed bit number using the short format. When a number is stored into a short it is converted to bit signed value. When we store bit data into memory it requires two bytes.
Since the memory systems on most computers are byte addressable a unique address for each byte , there are two possible ways to store in memory the two bytes that constitute the bit data. Freescale microcomputers implement the big endian approach that stores the most significant part first.
The ARM Cortex M processors implement the little endian approach that stores the least significant part first. Some ARM processors are biendian , because they can be configured to efficiently handle both big and little endian.
For example, assume we wish to store the 16 bit number 0x03E8 at locations 0x50,0x51, then. We also can use either the big or little endian approach when storing bit numbers into memory that is byte 8-bit addressable. If we wish to store the bit number 0x at locations 0xx53 then. In the above two examples we normally would not pick out individual bytes e. On the other hand, if each byte in a multiple byte data structure is individually addressable, then both the big and little endian schemes store the data in first to last sequence.
The Lilliputians considered the big endians as inferiors. The big endians fought a long and senseless war with the Lilliputians who insisted it was only proper to break an egg on the little end. A boolean number is has two states. The two values could represent the logical true or false.
The positive logic representation defines true as a 1 or high, and false as a 0 or low. If you were controlling a motor, light, heater or air conditioner the boolean could mean on or off.
In communication systems, we represent the information as a sequence of booleans: For black or white graphic displays we use booleans to specify the state of each pixel.