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240-334 Computer System Design Lecture 3

240-334 Computer System Design Lecture 3. Wannarat Suntiamorntut. Arithmetic for Computer. Implementing the Architecture. The numbers. Binary number (base 2) numbers are finite ( overflow ) fraction and real number

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240-334 Computer System Design Lecture 3

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  1. 240-334Computer System DesignLecture 3 Wannarat Suntiamorntut 240-334 By Wannarat

  2. Arithmetic for Computer • Implementing the Architecture 240-334 By Wannarat

  3. The numbers • Binary number (base 2) • numbers are finite (overflow) • fraction and real number • negative number e.g., No MIPS subi instruction, addi can add a negative number 240-334 By Wannarat

  4. Possible Representations Sign Magnitude One’s complement Two’s complement 000 = +0 000 = +0 000 = +0 001 = +1 001 = +1 001 = +1 010 = +2 010 = +2 010 = +2 011 = +3 011 = +3 011 = +3 100 = -0 100 = -3 100 = -4 101 = -1 101 = -2 101 = -3 110 = -2 110 = -1 110 = -2 111 = -3 111 = -0 111 = -1 Negative and Invert are different! 240-334 By Wannarat

  5. Addition & Subtraction • 7 - 6 {0111 - 0110} = 0001 • two’s complement 0111 + 1010 = 0001 • Overflow n-bit does not yield an n-bit number 0111 + 0001 1000 240-334 By Wannarat

  6. Detecting overflow • No overflow when add positive&negative • No overflow when signs are the same for subtraction • Overflow occur when : - add two positives yield a negative - add two negative gives a positive - subtract negative from positive and get negative - subtract positive from negative get a positive 240-334 By Wannarat

  7. Effect of Overflow • Exception occur (Interrupt) - control jumps to predefined address for exception - Interrupted address is saved • Don’t always to detect overflow - New MIPS instructions: addu, addiu ... 240-334 By Wannarat

  8. ALU • Build ALU support andi, ori instructions 240-334 By Wannarat

  9. Multiplexor • Select one of the inputs to be output, base on control input 240-334 By Wannarat

  10. ALU for Addition instruction • Cout = ab + bcin + acin • Sum = a xor b xor cin 240-334 By Wannarat

  11. ALU for Subtraction instruction • Two’s complement approach : just negative b and ADD 240-334 By Wannarat

  12. Supporting slt 240-334 By Wannarat

  13. 240-334 By Wannarat

  14. MIPS Arithmetic Instruction format 240-334 By Wannarat

  15. Conclusion ALU in MIPS • Use multiplexor to select output we want • efficiently perform subtraction using two’s complement • replicate 1-bit ALU to 32-bit ALU 240-334 By Wannarat

  16. Computation Problem :fast adder • 32-bit ALU faster than 1-bit ALU? • Carry-lookahead adder g = ab, p = a + b c1 = g0 + p0c0 c2 = g1 + p1c1c2 c3 = g2 + p2c2c3 ... 240-334 By Wannarat

  17. 240-334 By Wannarat

  18. Part II : Lecture III 240-334 By Wannarat

  19. Multiplication 0010 (multiplicand) x 1011 (multiplier) ???? 240-334 By Wannarat

  20. Unsign Combinational Multiplier 240-334 By Wannarat

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