2. Branch Addressing op rs rt address 4 1718 address beq $s1, $s2, Label if ($s1 = =$s2) go to Label 6 bits 5 bits 5 bits 16 bits effective 32 bit address = ( PC + 4 ) + ( address * 4 ) Next Instruction address is the relative number of instructions This is PC-relative addressing address * 4 = address : 00

3. Addressing in Jumps op address 2address jump j Label go to Label 6 bits 26 bits The complete 32 bit address is : address 00 4 bits 26 bits 2 bits Upper 4 bits of the Program Counter, PC jump uses word addresses This is Pseudodirect Addressing. Note: 256 MB word boundaries – 64M Instructions address * 4 = address:00

4. Where we've been: –Performance (seconds, cycles, instructions) –Abstractions: Instruction Set Architecture Assembly Language and Machine Language What's up ahead: –Implementing the Architecture

5. Sign Magnitude : One's Two's Complement Complement 000 = +0000 = +0000 = +0 001 = +1001 = +1001 = +1 010 = +2010 = +2010 = +2 011 = +3011 = +3011 = +3 100 = -0100 = -3100 = -4 101 = -1101 = -2101 = -3 110 = -2110 = -1110 = -2 111 = -3111 = -0111 = -1 Issues: balance, number of zeros, ease of operations Which one is best? Why? Possible Representations of Negative Numbers

6. Representing Numbers in Binary Consider n-1 bits n-1, n-2..., 3, 2, 1. ( bit n will be sign bit)

7. Representing Numbers in Binary Consider n-1 bits n-1, n-2..., 3, 2, 1. ( bit n will be sign bit) For positive numbers For negative numbers, use Two’s Complement, defined as

8. Representing Numbers in Binary For negative numbers, use Two’s Complement, defined as Two's Complement 000 = +0 001 = +1 010 = +2Binary 011 = +3 100 = -48 – 4= 4100 101 = -38 – 3= 5101 110 = -28 – 2= 6110 111 = -18 – 1= 7111

9. Representing Numbers in Binary Consider n-1 bits n-1, n-2..., 3, 2, 1. ( bit n will be sign bit) For negative numbers, use Two’s Complement 1 0 0 0... 0 - 1 0 1 1 1... 1

10. Representing Numbers in Binary Consider n-1 bits n-1, n-2..., 3, 2, 1. ( bit n will be sign bit) For negative numbers, use Two’s Complement

11. Representing Numbers in Binary Consider n-1 bits n-1, n-2..., 3, 2, 1. ( bit n will be sign bit) For negative numbers, use Two’s Complement

12. Representing Numbers in Binary Consider n-1 bits n-1, n-2..., 3, 2, 1. ( bit n will be sign bit) For negative numbers, use Two’s Complement

13. Representing Numbers in Binary Consider n-1 bits n-1, n-2..., 3, 2, 1. ( bit n will be sign bit) For negative numbers, use Two’s Complement Two’s Complement can be formed by Complementing each bit and adding 1.

14. Representing Numbers in Binary Consider n-1 bits n-1, n-2..., 3, 2, 1. ( bit n will be sign bit) For negative numbers, use Two’s Complement What is the Two’s Complement of a Negative Number?

15. Representing Numbers in Binary Consider n-1 bits n-1, n-2..., 3, 2, 1. ( bit n will be sign bit) For negative numbers, use Two’s Complement What is the Two’s Complement of a Negative Number? 2 n – 2 n – c = 2 n – 2 n + c = c Since

16. Two’s Complement Addition For x > 0 and y < 0

17. Two’s Complement Addition For x > 0 and y < 0

18. Two’s Complement Addition For x > 0 and y < 0

19. Two’s Complement Addition For x > 0 and y < 0 For x < 0 and y < 0 Normal addition works!

20. For n = 6 : weights : 32, 16, 8, 4, 2, 1 - 31 < numbers < +31 25 = 011001 100110 complement

21. For n = 6 : weights : 32, 16, 8, 4, 2, 1 - 31 < numbers < +31 25 = 011001 100110 complement -25 = 100111

22. For n = 6 : weights : 32, 16, 8, 4, 2, 1 - 31 < numbers < +31 25 = 011001 100110 complement -25 = 100111 = 2 -25 = 64 – 25 = 39 6

23. For n = 6 : weights : 32, 16, 8, 4, 2, 1 - 31 < numbers < +31 25 = 011001 100110 complement -25 = 100111 = 2 -25 = 64 – 25 = 39 15 = 001111 110000 complement -15 = 110001 6

24. For n = 6 : weights : 32, 16, 8, 4, 2, 1 - 31 < numbers < +31 25 = 011001 100110 complement -25 = 100111 = 2 -25 = 64 – 25 = 39 15 = 001111 110000 complement -15 = 110001 = 64 – 15 = 49 6

25. For n = 6 : weights 32, 16, 8, 4, 2, 1 - 31 < numbers < +31 25 = 011001 100110 complement -25 = 100111 = 2 -25 = 64 – 25 = 39 15 = 001111 110000 complement -15 = 110001 = 64 – 15 = 49 6 -25 + 15 100111 001111 110110

26. For n = 6 : weights 32, 16, 8, 4, 2, 1 - 31 < numbers < +31 25 = 011001 100110 complement -25 = 100111 = 2 -25 = 64 – 25 = 39 15 = 001111 110000 complement -15 = 110001 = 64 – 15 = 49 6 -25 + 15 100111 001111 110110 001010 -10

27. For n = 6 : weights 32, 16, 8, 4, 2, 1 - 31 < numbers < +31 25 = 011001 100110 complement -25 = 100111 = 2 -25 = 64 – 25 = 39 15 = 001111 110000 complement -15 = 110001 = 64 – 15 = 49 6 -25 + 15 100111 39 001111 15 110110 54 001010 64 - 54 -10

28. For n = 6 : weights 32, 16, 8, 4, 2, 1 - 31 < numbers < +31 25 = 011001 100110 complement -25 = 100111 = 2 -25 = 64 – 25 = 39 15 = 001111 110000 complement -15 = 110001 = 64 – 15 = 49 6 -25 + 15 100111 001111 110110 001010 -10 25 +(-15) 011001 110001 001010 +10

29. For n = 6 : weights 32, 16, 8, 4, 2, 1 - 31 < numbers < +31 25 = 011001 100110 complement -25 = 100111 = 2 -25 = 64 – 25 = 39 15 = 001111 110000 complement -15 = 110001 = 64 – 15 = 49 6 -25 + 15 100111 001111 110110 001010 -10 25 +(-15) 011001 110001 001010 +10 (-15)+(-14) 110001 110010 100011

30. For n = 6 : weights 32, 16, 8, 4, 2, 1 - 31 < numbers < +31 25 = 011001 100110 complement -25 = 100111 = 2 -25 = 64 – 25 = 39 15 = 001111 110000 complement -15 = 110001 = 64 – 15 = 49 6 -25 + 15 100111 001111 110110 001010 -10 25 +(-15) 011001 110001 001010 +10 (-15)+(-14) 110001 110010 100011 011101 - 29

31. For n = 6 : weights 32, 16, 8, 4, 2, 1 - 31 < numbers < +31 25 = 011001 100110 complement -25 = 100111 = 2 -25 = 64 – 25 = 39 15 = 001111 110000 complement -15 = 110001 = 64 – 15 = 49 6 -25 + 15 100111 001111 110110 001010 -10 25 +(-15) 011001 110001 001010 +10 (-15)+(-14) 110001 110010 100011 011101 - 29 (-25)+(-15) 100111 110001 011000 + 24???