There is one case in 16 bit 2's complement arithmetic whereīoth n and - n are negative, that is, n = -32768. Unsigned numbers, but it replicates the sign bit when applied to signed Right-shift operator shifts zeros into the high bit when applied to The change from unsigned to signed arithmetic. Note that the computation of d3 has also changed as a result of Of the 16-bit type used previously (only 9 bits were actually needed). Into nibbles allows us to use an 8-bit type for d0 instead By convention, these shouldĪs mentioned earlier, forcing n positive prior to breaking it down To represent signed 16-bit values and uint8_t In the above, we use the standard C type int16_t * the remainder of the code is unchanged */ To print signed values, we can replace the first few lines of the above Even so, adding these features to the code obscures the Results as soon as those results can be used to predict that digits willīe zero. Theįollowing fix is perhaps the cleanest, making effective use of partial Printing the significant digits, but this can be fixed in many ways. Of course, this code prints all 5 digits of n instead of only To represent unsigned 8 and 16-bit values. We use the standard C types uint8_t and uint16_t On machines with no divide instruction where speed is no issue, it mayīe better to simply use repeated subtraction instead of the fast butĪlgebraically complex code given in the body of this tutorial.Ĭonsider the following 16-bit conversion code as an example.įor ( b = '9' + 1 n = 0 n -= 100 ) ++c Numbers, for example, converting a 64-bit binary number to decimal on Of this tutorial examines how these methods can be extended to larger Techniques generalize in useful ways, for example, to the problem of doingĦ4 bit binary to decimal conversion using a 32 bit ALU. This situation is common on small microcontrollers, and the The focus of this tutorial is on writing fast code to convert unsigned 16 bitīinary numbers to decimal on a machine with an 8-bit ALU and no divide Hardware and because, even when such hardware is available, it is of littleĭirect use when dividing numbers larger than the ALU can handle. These assumptions are not always reasonable, bothīecause many commercially successful computers do not include division The arithmetic unit can conveniently do integer division yielding both a Unit is sufficiently large to handle the entire number n, and it assumes that The problem with this C code is that it assumes that the computer's arithmetic Suppose, forĮxample, you have an unsigned binary number that you wish to print out inĭecimal form. These problems have neverīeen insurmountable, but they are particularly annoying when writing programsįor machines with limited capacity in their arithmetic units. Numeric data should be represented in base 10. When dealing with textual input-output because of our convention that printed Programmers on binary computers have always faced computational problems Doing Without Hardware Multiply and Divide.Individuals may make single copiesįor their own use. This work may be transmitted or stored in electronic form on anyĬomputer attached to the Internet or World Wide Web so long as this T HE U NIVERSITY OF I OWA Department of Computer Scienceġ999, Douglas. Binary to Decimal Conversion in Limited Precision
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