1. COMPUTER ORGANIZATION ARITHMETIC YASSER MOHAMMAD

2. ADDITION  What is an overflow?  When can an overflow happen?  Add, addi, sub  exception on overflow  Addu and addiu  no exception ever  C compilers ALWAYS use u version. Why?

3. QUIZ  How to do arithmetic on bytes and half-words?

4. TESTING FOR OVERFLOW  Unsigned Numbers

5. MULTIPLICATION (1)

6. MULTIPLICATION (2)

7. SIGNED MULTIPLICATION  Run 31 iterations  Correct sign  Sign extend

8. PARALLEL MULTIPLICATION MIPS has mult and multu Results are stored in Hi and Lo To read the result use mflo

9. DIVISION MIPS has div and divu Remainder  Hi Qoutient  Lo Read using mflo and mfhi

10. MIPS ARITHMETICS REVISITED

11. FLOATING POINT REPRESENTATION

12. IEEE 754 b=127

13. IEEE 754 ENCODING

14. IEEE 754 EXAMPLE  Representing -0.75  Sign bit  Convert to binary  Shift fraction (mantisa) as needed adjusting the exponent  Find the exponent by adding the bias

15. QUIZ  Convert the following number to decimal:  1 1000011 0100000000000000000000

16. FLOATING POINT ADDITION  Match exponents  Add significands (mantissa)  Normalize the sum (1.xxxxx*….)  Round the number if necessary

17. EXAMPLE  0.5-7/16  Convert to binary  Find normalized forms  Match exponents  Add significands (mantissa)  Normalize the sum (1.xxxxx*….)  Round the number if necessary

18. MIPS FLOATING POINT REGISTERS

19. FLOATING POINT OPERATIONS

20. EXAMPLE float f2c (float fahr) { return ((5.0/9.0) *(fahr – 32.0)); //$F0 } f2c: lwc1 $f16,const5($gp) # $f16 = 5.0 (5.0 in memory) lwc1 $f18,const9($gp) # $f18 = 9.0 (9.0 in memory) div.s $f16, $f16, $f18 # $f16 = 5.0 / 9.0 lwc1 $f18, const32($gp)# $f18 = 32.0 sub.s $f18, $f12, $f18 # $f18 = fahr – 32.0 mul.s $f0, $f16, $f18 # $f0 = (5/9)*(fahr – 32.0) jr $ra # return $F12