ex start small with a 1-bit (half) adder A B Carry out Sum A 0 - PowerPoint PPT Presentation

Addition: ex start small with a 1-bit (half) adder A B Carry out Sum A 0 0 Sum 0 1 B 1 0 1 1 Carry out

Carry in ex 1-bit full adder A + Sum B Carry out n-bit addition: Sum i = A i + B i + CarryOut i-1 Need a bigger adder! A B Carry in Carry out Sum Carry in 0 0 0 0 0 1 A 0 1 0 Sum 0 1 1 B 1 0 0 1 0 1 Carry out 1 1 0 1 1 1

n-bit ripple-carry adder Carry in A 0 + Sum 0 B 0 A 1 + Sum 1 B 1 A 2 + Sum 2 B 2 … A n-1 + Sum n-1 B n-1 Carry out There are faster, more complicated ways too…

Processor Components 4 2 1 3 Instruction ALU Registers Memory Fetch and Decode

1 Arithmetic Logic Unit (ALU) a few bits Condition Codes (sign, overflow, carry-out, zero) word Operand A ALU words Result Operand B Operation a few bits Hardware unit for arithmetic and bitwise operations.

ex 1-bit ALU for bitwise operations Build an n-bit ALU from n 1-bit ALUs. Each bit i in the result is computed from the corresponding bit i in the two inputs. Op A B Result 0 0 0 Operation 0 0 1 A 0 1 0 0 MUX 0 1 1 Result 1 0 0 B 1 1 0 1 1 1 0 1 1 1

1-bit ALU Operation Carry in 2 A 0 MUX Result 1 Sum + 2 B Carry out

Carry in 2 Operation A 0 n-bit ripple carry adder 0 Result 0 MUX 1 Carry in Sum + B 0 2 A 0 + Sum 0 B 0 A 1 0 Result 1 MUX A 1 1 + Sum 1 Sum + B 1 2 B 1 A 2 + .... n-bit ALU … Sum 2 B 2 … A n-1 0 Result n-1 MUX A n-1 + 1 Sum n-1 Sum + B n-1 B n-1 2 Carry out Carry out

Carry in 2 ALU conditions Operation A 0 0 Result 0 MUX 1 Extra ALU outputs Sum + B 0 2 describing properties of result. A 1 Zero Flag: 0 Result 1 MUX 1 if result is 00...0 else 0 1 Sum + Sign Flag: B 1 2 1 if result is negative else 0 .... … Carry Flag: 1 if carry out else 0 (Signed) Overflow Flag: A n-1 0 Result n-1 1 if signed overflow else 0 MUX 1 Sum + B n-1 2 Implement these. Carry out

Operation 2 Add subtraction A 0 0 Result 0 MUX 1 How can we control ALU inputs B 0 + 0 2 or add minimal new logic 1 to compute A-B ? A 1 0 Result 1 MUX 1 + B 1 0 2 1 .... .... … A n-1 0 Result n-1 MUX 1 + B n-1 0 2 1 Carry out

Operation Negate B Invert A A NAND B 2 A 0 0 0 1 Result 0 MUX 1 A NOR B B 0 + 0 2 1 A 1 0 0 1 A<B Result 1 MUX 1 + B 1 0 2 1 A==B .... .... .... … A n-1 0 0 1 Result n-1 MUX How can we control ALU inputs 1 or add minimal new logic + B n-1 0 ex to compute each? 2 1 Carry out

Controlling the ALU Condition Codes ALU control lines Function 0000 AND Operand A 0001 OR ALU Result 0010 add Operand B 0110 subtract 1100 NOR Control Lines

ex start small with a 1-bit (half) adder A B Carry out Sum A 0 - PowerPoint PPT Presentation

Addition: ex start small with a 1-bit (half) adder A B Carry out Sum A 0 0 Sum 0 1 B 1 0 1 1 Carry out Carry in ex 1-bit full adder A + Sum B Carry out n-bit addition: Sum i = A i + B i + CarryOut i-1 Need a bigger adder!

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