TK2633 : MICROPROCESSOR & INTERFACING

1. TK2633 : MICROPROCESSOR & INTERFACING Lecture 10: Fixed Point Arithmetic Lecturer: Ass. Prof. Dr. Masri Ayob

2. Fixed Point Arithmetic. • 8-bit binary addition. • Suppose that the ten 8-bit numbers, stored at memory locations 2800H through 2809H, are added. • To sum these data, an 8-bit instructions are chosen. • The ADD M instruction is chosen. • Since this is to add 10 numbers, the programme loop construct is ideal for this problem. • Figure illustrates the flowchart to tackle the problem. Written by: Ramizi Mohamed, Edited by:Dr Masri Ayob

3. 8-bit binary addition • The 8-bit binary addition listed in the example below, results in a problem that the largest sum can be only 0FFH. • This sum is appropriate only if 10 numbers are small, therefore to avoid overflow for bigger sum operation, the 16-bit sum operation will take place. Written by: Ramizi Mohamed, Edited by:Dr Masri Ayob

4. 8-bit binary addition • Example of 16-bit summation. Written by: Ramizi Mohamed, Edited by:Dr Masri Ayob

5. 8-bit binary subtraction • Suppose that two lists of numbers, each 10H bytes long, appear in the memory to be subtracted. • A programme must take the number stored at LIST2 and subtract it from the number stored at LIST1. • The difference must be stored at a location in LIST2. • This operation repeats 10H times until all sets of numbers are subtracted. • Figure illustrates the process. Written by: Ramizi Mohamed, Edited by:Dr Masri Ayob

6. 8-bit binary subtraction: Exercise • There are two lists of numbers (LIST1 and LIST2), each 10H bytes long, appear in the memory. Write a program to take the number stored at LIST2 and subtract it from the number stored at LIST1. The difference must be stored at a location in LIST2. Written by: Ramizi Mohamed, Edited by:Dr Masri Ayob

7. Unsigned Multiplication by Repeated Addition • Repeated addition is the simplest method of multiplication to understand. • Suppose to multiply two 8-bit numbers, one number can be used as the loop counter. • The other number can be added the number of times stored in the loop counter. • Figure illustrates how the number 6 can be multiplied by 3. Written by: Ramizi Mohamed, Edited by:Dr Masri Ayob

8. Unsigned Multiplication by Repeated Addition Written by: Ramizi Mohamed, Edited by:Dr Masri Ayob

9. Unsigned Constant Multiplication • Instead of using the repeated addition technique presented earlier, another technique often results in a much faster multiplication, which using DAD instruction. • The easiest way to multiply by 4 is by using the DAD H instruction. • Remember that if double HL twice, it is multiplied by 4. • Example : Written by: Ramizi Mohamed, Edited by:Dr Masri Ayob

10. Unsigned Multiplication Algorithm • The most flexible version of multiplication is the unsigned multiplication shift and add algorithm. • Observe the example below, the unsigned multiplication is a combination of shifting the number followed by addition for every shifted number. • Figure below, illustrates the process of shifting and adding number 9 and 15. Written by: Ramizi Mohamed, Edited by:Dr Masri Ayob

11. Unsigned Multiplication Algorithm • The flowchart example to perform the algorithm. Written by: Ramizi Mohamed, Edited by:Dr Masri Ayob

12. Unsigned Multiplication Algorithm Written by: Ramizi Mohamed, Edited by:Dr Masri Ayob

13. Written by: Ramizi Mohamed, Edited by:Dr Masri Ayob

14. Signed Multiplication • Modified Flowchart diagram to perform signed multiplication. Written by: Ramizi Mohamed, Edited by:Dr Masri Ayob

15. Signed Multiplication • To do the signed multiplication, the multiplicand and multiplier are exclusive ORed together. • The result, which indicates the sign of the product, is saved in the B register. • Both numbers are then adjusted so that they are positive before the MULT subroutine is called. • Upon returning from the MULT subroutine, the sign of the B register shows the sign of the product. • For a negative result, the product in the HL register pair must be negated to form a negative product. • For a positive result, the product does not change. Written by: Ramizi Mohamed, Edited by:Dr Masri Ayob

16. Signed Multiplication: Modification of the previous program Written by: Ramizi Mohamed, Edited by:Dr Masri Ayob

17. Division by a constant • If data are shifted to the left, they multiply by 2 for each bit position of the shift. • If data are shifted to the right, they divide by 2 for each bit position of the shift. • Knowing this as a technique used to multiply by a constant, a technique can be developed so that a number can be divided by any power of 2. Written by: Ramizi Mohamed, Edited by:Dr Masri Ayob

18. Written by: Ramizi Mohamed, Edited by:Dr Masri Ayob

19. Signed division by a constant • Example shows how the signed contents of the accumulator are divide by 4 with the result rounded. • Notice that a shift left copies the sign bit into the carry flag before shifting right twice. Written by: Ramizi Mohamed, Edited by:Dr Masri Ayob

20. Unsigned division algorithm • To divide a number by any integer value, a division algorithm is normally used to develop a subroutine. The division algorithm uses a combination of shifting left, comparing, subtracting, and setting bits to perform binary division. • Below is an illustration of division algorithm. Written by: Ramizi Mohamed, Edited by:Dr Masri Ayob

21. Unsigned division algorithm Written by: Ramizi Mohamed, Edited by:Dr Masri Ayob

22. Unsigned division algorithm Written by: Ramizi Mohamed, Edited by:Dr Masri Ayob

23. Signed division algorithm • Signed binary division is treated in the same manner as signed multiplication. Written by: Ramizi Mohamed, Edited by:Dr Masri Ayob

24. Thank youQ&A Written by: Ramizi Mohamed, Edited by:Dr Masri Ayob