1. 1 Signed Arithmetic Logical Operations Ellen Spertus MCS 111 October 1, 2002

2. 2 Homework 5: 1 a[0] = a[0] + a[1] - a[2]; lw $a0, __($t0) lw $a1, __($t0) lw $a2, __($t0) add $t1,, sub $t2, $t1, sw $t2, __($t0) Diagram assumes Big-Endian

3. 3 Homework 5: 2 foo(int i, int j) { int temp; temp = a[i]; a[i] = a[j]; a[j] = temp; return; }

4. 4 From representation to value 1000

5. 5 Today Review: unsigned numbers Signed numbers MIPS instructions for signed and unsigned instructions Character encoding Logical operations

6. 6 Unsigned binary arithmetic Biggest number? Smallest number?

7. 7 Signed binary arithmetic (two’s complement) Sign bit Biggest number? Smallest number?

8. 8 Signed binary to decimal

9. 9 Shortcut To negate a number –Invert each bit –Add 1 Practice –1001  0110  0111 (7 10 ), so the original was -7 –1111 –1000

10. 10 Relative sizes Which 4-bit number is bigger: 1000 or 0111? –Signed comparison –Unsigned comparison

11. 11 Sign extension The number 7 10 0111 00000111 0000000000000111 The number -1 10 1111 11111111 1111111111111111 Extend the sign bit all the way to the left.

12. 12 A closer look at load-byte (lb) load byte signed (lb) –Treat the byte as a signed number –Sign extend it to word length –lb $t0, 400($zero) load byte unsigned (lbu) –Treat the byte as an unsigned number –Zero extend it to word length –lbu $t0, 400($zero)

13. 13 MIPS instructions Signed numbers –set less than (slt) –set less than immediate (slti) –load byte (lb) Unsigned numbers –set less than unsigned (sltu) –set less than immediate unsigned (sltiu) –load byte unsigned (lbu) a0 = 11111111111111111111111111111111 two a1 = 00000000000000000000000000000000 two slt $t0, $a0, $a1 # signed comparison sltu $t1, $a0, $a1 # unsigned comparison

14. 14 How do we add signed numbers? Just like we always have! signed unsigned -128 64 32 16 8 4 2 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1

15. 15 What about overflow? signed unsigned -128 64 32 16 8 4 2 1 0 1 1 1 1 1 1 1

16. 16 Definition of overflow When a carry bit flows into the sign bit This can only happen with signed arithmetic Machine raises an exception

17. 17 MIPS instructions (2) Signed numbers –set less than (slt) –set less than immediate (slti) –load byte (lb) –add –add immediate (addi) –sub –subtract immediate (subi) Unsigned numbers –set less than unsigned (sltu) –set less than immediate unsigned (sltiu) –load byte unsigned (lbu) –add unsigned (addu) –add immediate unsigned (addiu) –subtract unsigned (subu) –subtract immediate unsigned (subiu)

18. 18 Pseudo-instructions Definition: Instructions converted by the assembler into real machine instructions Examples: –Load immediate: li $r1, 5 is replaced by: –Subtract immediate: subi $r1, $r1, 5 is replaced by:

19. 19 Differences between signed and unsigned instructions Sign extension vs. Zero extension –lb/lbu Whether to signal overflow/underflow –add/addu, addi/addiu, sub/subu How to compare numbers –slt/sltu, slti/sltiu

20. 20 Remainder of today Logical operations –Bitwise operations –Shifting

21. 21 Bitwise operations Perform the operation on each bit position Practice –Initial values $t0 =..00000111 $t1 =..00000001 –Problems not $t2, $t0 and $t2, $t0, $t1 or $t2, $t0, $t1

22. 22 Shifting Assume $t0 = 0..00001100 Shift left logical (sll) –sll $t1, $t0, 2 –result: Shift right logical (srl) –srl $t1, $t0, 2 –result: Note: Zeroes are shifted in