8051 Arithmetic Operations Subtraction, Multiplication, Division, Decimal Arithmetic ,Example Programs, AND Summary

Subtraction

Subtraction can be done by taking the 2’s complement of the number to be subtracted, the subtrahend, and adding it to another number, the minuend. The 8051, however, has com­mands to perform direct subtraction of two signed or unsigned numbers. Register A is the destination address for subtraction. All four addressing modes may be used for source addresses. The commands treat the carry flag as a borrow and always subtract the carry flag as part of the operation.

The following table lists the subtract mnemonics.

Note that the C flag is set if a borrow is needed into bit 7 and reset otherwise. The AC flag is set if a borrow is needed into bit 3 and reset otherwise. The OV flag is set if there is a borrow into bit 7 and not bit 6 or if there is a borrow into bit 6 and not bit 7. As in the case for addition, the OV Flag is the XOR of the borrows into bit positions 7 and 6.

Unsigned and Signed Subtraction

Again, depending on what is needed, the programmer may choose to use bytes as signed or unsigned numbers. The carry flag is now thought of as a borrow flag to account for situations when a larger number is subtracted from a smaller number. The OV flag indi­cates results that must be adjusted whenever two numbers of unlike signs are subtracted and the result exceeds the planned signed magnitudes.

Unsigned Subtraction

Because the C flag is always subtracted from A along with the source byte, it must be set to 0 if the programmer does not want the flag included in the subtraction. If a multi-byte subtraction is done, the C flag is cleared for the first byte and then included in subsequent higher byte operations.

The result will be in true form, with no borrow if the source number is smaller than A, or in 2’s complement form, with a borrow if the source is larger than A. These are not signed numbers, as all eight bits are used for the magnitude. The range of numbers is from positive 255d (C = 0, A= FFh) to negative 255d (C = I, A= 0th).

The following example demonstrates subtraction of larger number from a smaller number:

015d = 0000111 lb

SUBB  100d = 01 01100100b

-085d  1 10101011b= 171d

The C flag is set to I, and the OV flag is set to 0. The 2’s complement of the result is 085d.

The reverse of the example yields the following result:

100d = 01100100b

015d = 00001111b

085d 01010101b = 085d

The C flag is set to 0, and the OV flag is set to 0. The magnitude of the result is in true form.

Signed Subtraction

As is the case for addition, two combinations of unsigned numbers are possible when sub­tracting: subtracting numbers of like and unlike signs. When numbers of like sign are subtracted, it is impossible for the result to exceed the positive or negative magnitude limits of +I 27d or – I 28d, so the magnitude and sign of the result do not need to be adjusted, as shown in the following example:

+ 100d = 01100100b    (Carry flag = 0 before SUBB)

SUBB +126d = 0111110b

-026d    11100110b = -026d

There is a borrow into bit positions 7 and 6; the carry flag is set to I, and the OV flag is cleared.

The following example demonstrates using two negative numbers:

-061d = 1100001 lb  (Carry flag = 0 before SUBB)

SUBB -116d = 11000011b

+055d 00110111b = +55d

There are no borrows into bit positions 6 or 7, so the OY and carry flags are cleared to zero.

An overflow is possible when subtracting numbers of opposite sign because the situa­tion becomes one of adding numbers of like signs, as can be demonstrated in the following example:

-099d = 10011101b   (Carry flag = 0 before SUBB)

SUBB + 100d = 01 01100100b

-199d 00111001b = +057d

Here, there is a borrow into bit position 6 but not into bit position 7; the OV flag is set to I, and the carry flag is cleared to 0. Because the OV flag is set to I, the result must be adjusted. In this case, the magnitude can be interpreted as the 2’s complement of 7 ld, the remainder after a carry out of l 28d from I 99d. The magnitude is correct, and the sign needs to be corrected to a 1 .

The following example shows a positive overflow:

+087d = 0101011 lb   (Carry flag = 0 before SUBB)

SUBB -052d = 11001100b

+139d    1000101 lb = -I 17d

There is a borrow from bit position 7, and no borrow from bit position 6; the OV flag and the carry flag are both set to I. Again the answer must be adjusted because the OV flag is set to one. The magnitude can be interpreted as a +01 Id, the remainder from a carry out of I 28d. The sign must be changed to a binary 0 and the OV condition dealt with.

The general rule is that if the OV flag is set to I, then complement the sign bit. The OV flag also signals that the result is greater than – I 28d or +I 27d.

Again, it must be emphasized: When an overflow occurs in a program, an error has been made in the estimation of the largest number needed to successfully operate the pro­gram. Theoretically, the program could resize every number used, but this extreme proce­dure would tend to hinder the performance of the microcontroller.

Note that for all the examples in this section, it is assumed that the carry flag = 0 before the SUBB. The carry flag must be 0 before any SUBB operation that depends upon C = 0 is done.

The following table lists examples of SUBB multiple-byte signed arithmetic operations:

CAUTION

Remember to set the carry flag to zero if it is not to be included as part of the subtraction operation.

 Multiplication and Division

The 8051 has the capability to perform 8-bit integer multiplication and division using the A and B registers. Register B is used solely for these operations and has no other use except as a location in the SFR space of RAM that could be used to hold data. The A register holds one byte of data before a multiply or divide operation, and one of the result bytes after a multiply or divide operation.

Multiplication and division treat the numbers in registers A and B as unsigned. The programmer must devise ways to handle signed numbers.

Multiplication

Multiplication operations use registers A and B as both source and destination addresses for the operation. The unsigned number in register A is multiplied by the unsigned number in register B, as indicated in the following table:

The OV flag will be set if Ax B > FFh. Setting the OV flag does not mean that an error has occurred. Rather, it signals that the number is larger than eight bits, and the program­mer needs to inspect register B for the high-order byte of the multiplication operation. The carry flag is always cleared to 0.

The largest possible product is FEO I h when both A and B contain FFh. Register A contains 0lh and register B contains FEh after multiplication of FFh by FFh. The OV flag is set to 1 to signal that register B contains the high-order byte of the product; the carry flag is 0.

The following table gives examples of MUL multiple-byte arithmetic operations:

CAUTION

Note there is no comma between A and 8 in the MUL mnemonic.

Division

Division operations use registers A and B as both source and destination addresses for the operation. The unsigned number in register A is divided by the unsigned number in regis­ter B, as indicated in the following table:

The OV flag is cleared to 0 unless B holds 00h before the DIV. Then the 0V flag is set to I to show division by 0. The contents of A and B, when division by 0 is attempted, are undefined. The carry flag is always reset.

Division always results in integer quotients and remainders, as shown in the following example:

When done in hex:

The following table lists examples of DIV multiple-byte arithmetic operations:

CAUTION

The original contents of B (the divisor) are lost.

Note there is no comma between A and B in the DIV mnemonic.

Decimal Arithmetic

Most 8051 applications involve adding intelligence to machines where the hexadecimal numbering system works naturally. There are instances, however, when the application involves interacting with humans, who insist on using the decimal number system. In such cases, it may be more convenient for the programmer to use the decimal number system to represent all numbers in the program.

Four bits are required to represent the decimal numbers from 0 to 9 (0000 to 1001) and the numbers are often called Binary coded decimal (BCD) numbers. Two of these BCD numbers can then be packed into a single byte of data.

The 8051 does all arithmetic operations in pure binary. When BCD numbers are being used the result will often be a non-BCD number, as shown in the following example:

Note that to adjust the answer, an 06d needs to be added to the result.

The opcode that adjusts the result of BCD addition is the decimal adjust A for addi­tion (DA A) command, as shown in the following table:

The C flag is set to I if the adjusted number exceeds 99BCD and set to 0 otherwise. The DA A instruction makes use of the AC flag and the binary sums of the individual binary nibbles to adjust the answer to BCD. The AC flag has no other use to the programmer and no instructions-other than a MOV or a direct bit operation to the PSW-affect the AC flag.

It is important to remember that the DA A instruction assumes the added numbers were in BCD before the addition was done. Adding hexadecimal numbers and then using DA A will not convert the sum to BCD.

The DA A opcode only works when used with ADD or ADDC opcodes and does not give correct adjustments for SUBB, MUL or DIV operations. The programmer might best consider the ADD or ADDC and DA A as a single instruction and use the pair automat­ically when doing BCD addition in the 8051.

The following table gives examples of BCD multiple-byte arithmetic operations:

CAUTION

All numbers used must be in BCD form before addition. Only ADD and ADDC are adjusted to BCD by DA A.

Example Programs

The challenge of the programs presented in this section is writing them using only opcodes that have been covered to this point in the book. Experienced programmers may long for some of the opcodes to be covered in Chapter 6, but as we shall see, programs can be written without them.

EXAMPLE PROBLEM 5.1

Add the unsigned numbers found in internal RAM locations 25h, 26h, and 27h together and put the result in RAM locations 30h (MSB) and 3lh (LSB).

• Thoughts on the Problem The largest number possible is FFh + FFh = 01 FEh + FFh = 02FDh, so that two bytes will hold the largest possible number. The MSB will be set to 0 and any carry bit added to it for each byte addition.

To solve this problem, use an ADD instruction for each addition and an ADDC to the MSB for each carry which might be generated. The first ADD will adjust any carry flag which exists before the program starts.

The complete program is shown in the following table:

COMMENT

Notice how awkward it becomes to have to use the A register for all operations. Jump instruc­tions, which will be covered in Chapter 6, require less use of A.

EXAMPLE PROBLEM 5.2

Repeat problem 5.1 using BCD numbers.

• Thoughts on the Problem The numbers in the RAM locations must be in BCD before the problem begins. The largest number possible is 99d + 99d = I 98d + 99d = 297d, so that up to two carries can be added to the MSB.

The solution to this problem is identical to that for unsigned numbers, except a DA A must be added after each ADD instruction. If more bytes were added so that the MSB could exceed 09d, then a DA A would also be necessary after the ADDC opcodes.

The complete program is shown in the following table:

COMMENT

When using BCD numbers, DA A can best be thought of as an integral part of the ADD instructions.

EXAMPLE PROBLEM 5.3

Multiply the unsigned number in register R3 by the unsigned number on port 2 and put the result in external RAM locations 10h (MSB) and 11 h (LSB).

• Thoughts on the Problem The MUL instruction uses the A and B registers; the prob­lem consists of MOV es to A and B followed by MOVes to the external RAM. The com­plete program is shown in the following table:

coMMENT

Again we see the bottleneck created by having to use the A register for all external data transfers.

More advanced programs which do signed math operations and multi-byte multiplication and division will have to wait for the development of Jump instructions in Chapter 6.

Summary OF 8051 Arithmetic Operations

The 8051 can perform all four arithmetic operations: addition, subtraction. multiplication, and division. Signed and unsigned numbers may be used in addition and subtraction; an 0Y flag is provided to signal programmer errors in estimating signed number magnitudes needed and to adjust signed number results. Multiplication and division use unsigned numbers. BCD arithmetic may be done using the DA A and ADD or ADDC instructions.

The following table lists the arithmetic mnemonics: