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Author: Admin | 2025-04-28
Input){ data=input+1; return data;}8-bitsigned numbersIf a byte is used to representa signed 2’scomplement number, then thevalue of the number isN = -128•b7 +64•b6 + 32•b5 + 16•b4 + 8•b3 +4•b2 + 2•b1 + b0There are also 256 differentsigned 8 bit numbers. The smallest signed 8-bit number is -128 and thelargest is 127. For example, 100000102is -128+2 or -126. Other examples are shown in the following table. binary hex Calculation decimal 00000000 0x00 0 01000001 0x41 64+1 65 00010110 0x16 16+4+2 22 10000111 0x87 -128+4+2+1 -121 11111111 0xFF -128+64+32+16+8+4+2+1 -1 Table 3-5. Exampleconversions from signed 8-bit binary to hexadecimal and to decimal.For the signed 8-bit numbersystem the basis is{ 1, 2, 4, 8, 16, 32, 64, -128}Observation: The mostsignificant bit in a 2’s complement signed number willspecify the sign. Notice that the same binarypattern of 111111112could represent either 255 or -1. It is very important for the softwaredeveloper to keep track of the number format. The computer can notdetermine whether the 8-bit number is signed or unsigned. You, as theprogrammer, will determine whether the number is signed or unsigned bythe specific assembly instructions you select to operate on the number.Some operations like addition, subtraction, and shift left (multiply by2) use the same hardware (instructions) for both unsigned and signedoperations. On the other hand, multiply, divide, and shift right(divide by 2) require separate hardware (instruction) for unsigned andsigned operations. The compiler willautomatically choose the proper implementation.It is always good programmingpractice to have clear understanding of the data type for each number,variable, parameter, etc. For some operations there is a differencebetween the signed and unsigned numbers while for others it does notmatter. signeddifferent from unsigned signedsame as unsigned /% division + addition * multiplication - subtraction > greaterthan == isequal to lessthan | logicalor >= greaterthan or equal to & logicaland lessthan or equal to ^ logicalexclusive or >> rightshift leftshift Table 3-6. Operationseither depend or don't depend on whether the number is signed/unsigned.The point is that care must betaken when dealing with a mixture of numbers of different sizes andtypes.Similar to the unsignedalgorithm, we can use the basis to convert a decimal number into signedbinary. We will work through the algorithm with the example ofconverting -100 to 8-bit binary. We with the largest basis element (inthis case -128) and decide do we need to include it to make -100. Yes(without -128, we would be unable to add the other basis elementstogether to get any negative result), so we set bit 7 and subtract thebasis element from our value. Our new value is -100 minus -128, whichis 28. We go the next largest basis element, 64 and ask do we need it.We do not need 64 to generate our 28, so bit6 is zero. Next we go thenext basis element, 32 and ask do we need it. We do not need 32 togenerate our 28, so bit5 is zero. Now we need the basis element 16, sowe set bit4, and subtract 16 from our number 28 (28-16=12). Continuingalong, we need basis elements 8
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