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CS 230: Computer Organization and Assembly Language. Aviral Shrivastava. Department of Computer Science and Engineering School of Computing and Informatics Arizona State University. Slides courtesy: Prof. Yann Hang Lee, ASU, Prof. Mary Jane Irwin, PSU, Ande Carle, UCB. Announcements. Quiz 2
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CS 230: Computer Organization and Assembly Language Aviral Shrivastava Department of Computer Science and Engineering School of Computing and Informatics Arizona State University Slides courtesy: Prof. Yann Hang Lee, ASU, Prof. Mary Jane Irwin, PSU, Ande Carle, UCB
Announcements • Quiz 2 • Project 2 • Quiz 3 • Thursday, Oct 06, 2009 • Complete Chapter 3 • Project 3 • Implement an assembler
Multiplication Multiplicand 1 0 0 0Multiplier x 1 0 0 1 -------------- 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ------------------Product 1 0 0 1 0 0 0 • Binary makes it easy • Multiplier bit = 0 place 0 • Multiplier bit = 1 place multiplicand • (232-1)*(232-1) = 264 – 2.232 + 1 – need 64-bits
Multiplication Multiplicand 1 0 0 0Multiplier x 1 0 0 1 -------------- 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ------------------Product 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 x 1 0 0 1---------------------------------- 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ----------------------- 0 1 0 0 1 0 0 0 What should be added in each step Shift left Shift right Multiplicand Multiplier 64-bit Test Add 64-bit ALU Control Write Product 64-bit
Multiplication 0 0 0 0 1 0 0 0 x 1 0 0 1------------------------------------- 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ----------------------- 0 1 0 0 1 0 0 0 1. Initialize 2. Test, Add, Write 3. Shift left multiplicand, shift right multiplier 4. Test 5. Shift left multiplicand, shift right multiplier 6. Test 7. Shift left multiplicand, shift right multiplier 8. Test, Add, Write 9. Shift left multiplicand, shift right multiplier 10. Done Shift left Shift right 1001 01000000 00100000 00010000 10000000 00001000 0000 0001 0100 0010 8-bit 4-bit Test Add Control Write 01001000 00001000 00000000 8-bit
Multiply Algorithm 2 Multiplicand 1 0 0 0Multiplier x 1 0 0 1 -------------- 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ------------------Product 1 0 0 1 0 0 0 1 0 0 0 x 1 0 0 1------------------------------------ 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 ----------------------- 0 1 0 0 1 0 0 0 Partial Product at each step Shift right Multiplicand Multiplier 32-bit Test Add 32-bit ALU Control Write Product 64-bit Shift right
Multiply Algorithm 2 1 0 0 0 x 1 0 0 1---------------------------- 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 ----------------------- 0 1 0 0 1 0 0 0 1. Initialize 2. Test, Add 3. Shift product right, shift multiplier right 4. Test 5. Shift product right, shift multiplier right 6. Test 7. Shift product right, shift multiplier right 8. Test, Add 9. Shift product right, shift multiplier right 10. Done Shift right 1000 0010 0100 1001 0000 0001 4-bit 4-bit Test Add Control Write 01000000 00010000 00000000 10010000 10000000 00100000 01001000 8-bit Shift right
Multiply Algorithm 2* 1 0 0 0 x 1 0 0 1------------------------------------- 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 ----------------------- 0 1 0 0 1 0 0 0 Multiplicand 32-bit Add 32-bit ALU Control Write Test Multiplier 64-bit Shift right
Multiplication • multu $rs $rt • Has 2 sources (32-bit registers) • No explicit destination • Has 2 implicit destinations • $hi – upper 32-bits • $lo – lower 32-bits • Have to explicitly read these registers • mflo $rd • Moves from $lo to $rd • mfhi $rd • Moves from $hi to $rd • Also mult – signed multiply • Multiply & then take care of the sign separately
Division Divisor 1000 Quotient 1001 Dividend: 1001010 0001010 0001010 0001010 0000010 Remainder 1001 Quotient --------------- Divisor 1000 | 1001010 - 1000 ----------- 10 101 1010 -1000 --------- 10 Remainder Shift right Shift left Divisor Quotient 64-bit 32-bit Subtract 64-bit ALU Control Write Remainder 64-bit Test
Division 1001 Quotient --------------- Divisor 1000 | 1001010 - 1000 ----------- 10 101 1010 -1000 --------- 10 Remainder 1. Initialize 2. Subtract & test 3. Restore remainder, push 0 in quotient, shift divisor right 4. Subtract & test 5. Push 1 in quotient, shift divisor right 6. Subtract & test 7. Restore remainder, push 0 in quotient, shift divisor right 8. Subtract & test 9. Restore remainder, push 0 in quotient, shift divisor right 10. Subtract & test 11. Push 1 in quotient, shift divisor right 12. Done Shift right Shift left 10000000 0001 01000000 00010000 00100000 00000100 00001000 0100 1001 0000 0010 8-bit 4-bit Add/Sub 64-bit ALU Control Write 11001010 11101010 00001010 11111010 00001010 01001010 00000010 01001010 00001010 8-bit Test
Division • div, divu • $lo = $rs/$rt; $hi = $rs%$rt • Need mflo and mfhi • Transfer results of div to normal registers • Signed Division • Calculate the sign bit separately
Improved Division • Instead of shifting divisor right • Shift remainder to left • Use the least significant bits of remainder to store the quotient Divisor 32-bit Add 32-bit ALU Control Write Remainder 64-bit Shift right
Yoda says… • Luke: I can’t believe it. • Yoda: That is why you fail
