Файл: Microcontroller Programming. Thi Micro Chip PIC (Julio Sanchez, 2007).pdf

Microcontrollers usually support the fundamental operations of addition and subtraction on signed and unsigned integer operands with a single primitive operation. The addition and subtraction operators in lowand mid-range devices allow two operands. The more powerful microcontrollers support addition and subtraction of three operands, which is useful in implementing multi-digit routines. In either case, the software determines if the result is signed or unsigned by interpreting the changes in the high-order bit of the operands and by evaluating the status flags if these are available.

4.2.2 Operations on Decimal Numbers

Although microcontrollers are binary devices, the instruction set often includes operations for performing arithmetic on binary coded decimal numbers. In Chapter 3 we saw that BCD numbers can be stored in packed or unpacked form. In packed format two BCD digits are contained in each byte. The low-order BCD digit takes up bits 0 to 3 and the high-order BCD digit takes up bits 4 to 7. Unpacked BCD digits are stored one digit per byte; in this case the high-order nibble is unused. The packed and unpacked binary coded decimal formats can be seen in Figure 3-9.

Microcontroller designers usually adopt the packed BCD format for representing decimal operands. One advantage of packed BCDs is that the two decimal digits encoded in a single byte can be represented as hexadecimal digits. For example, the values H24 and H99 represent the packed BCD digits 24 and 99 respectively. Note that each hex digit is preceded by the letter H to indicate radix 16. In actual microcontroller programming other ways are often used for representing numbers in hexadecimal notation.

The addition and subtraction of decimal numbers represented in packed BCD can be performed with binary primitive operations, complemented with some additional adjustments. In some cases the addition of two BCD numbers in packed format may produce a valid result, for example:

In the previous examples the results are valid because the sum of each digit does not exceed the range of the BCD format. However, the following additions do not produce valid BCD results:

In the case of the first operation the valid BCD result would be: 33 + 27 = 60, in the second one 31 + 59 = 90, and in the third one 56 + 27 = 83. A simple adjustment corrects the error, as follows:

In all three cases adding 6 to the previous sum produces the expected result. The logic for deciding when the value 6 must be added is simple: if the sum of the low-order digit is greater than 9 or if the sum produced a carry out of the low-order nibble, then add 6 to the sum to perform the decimal adjustment. Some high-end microcontrollers contain a primitive instruction that executes the decimal adjustment automatically, that is, without having to test the sum. However, this instruction is not available in lowand mid-range devices.

Also note that the largest number that can be encoded in packed BCD format is the decimal 99. When adding two BCD digits the high-order digit of the sum cannot be greater than 9. If so, then the capacity of the format has been exceeded and the result cannot be adjusted by the simple addition of 6. Here again, a multi-byte processing routine can be developed in order to accommodate the result of BCD addition when the sum exceeds a single byte.

Many microcontrollers are equipped with a flag that indicates overflow from binary digit number 3. This flag, sometimes called the digit carry or the half carry flag, can be used to detect that a calculation has overflowed the storage capacity of four binary digits. The availability of this flag simplifies the logic necessary for adjusting binary addition of decimal operands since the value 6 must be added when the digit in the low-order nibble is larger than 9, or when there has been a carry to the next digit. The following flowchart shows this processing.

START

A = FIRST PACKED BCD

B = SECOND PACKED BCD

PERFORM C = A + B

Figure 4-1 Flowchart for Two-byte BCD Addition

4.3 Bit Manipulations and Auxiliary Operations

In addition to basic logic and arithmetic, microcontrollers contain primitive operators to manipulate individual bits, to compare operands, to make decision based on the state of individual bits and flags, and to convert data to other formats. As always, presence or absence of some of these operations, as well as their degree of power and sophistication, varies with the individual microcontroller. In the following subsections we describe the most commonly available primitives.

4.3.1 Bit Shift and Rotate

The fundamental operators to shift and rotate are useful in developing BCD and binary arithmetic routines. One interesting use of bit shifting is in implementing binary multiplication and division routines.

Shift operations consist of transposing to the left or right all the bits in the operand. In microcontrollers the operand is usually a processor register. For example, after a right shift operation all the bits in the value 01110101B (75H) are moved one position to the right, resulting in the value 00111010B (3AH). Note that on a right shift the right-most bit disappears and a zero comes into the high-order bit. By the same token, in a left shift the high-order bit disappears and a zero comes into the low-order bit. Figure 4-2 shows the action of a left-shift operation.

Figure 4-2 Left Shift Operation

The rotate operation differs from the shift in that in the rotate the low-order bit is either a copy of the high-order bit or of the carry flag. In the first case the operation is a pure rotate, in the second case the rotate is referred to as rotate-through-carry. Figure 4-3 shows the action of a left-rotate-through-carry flag.

7 6 5 4 3 2 1 0

FIRST STEP

CF 7 6 5 4 3 2 1 0

7 6 5 4 3 2 1 0

Figure 4-3 Rotate-through-carry Left Operation