Building the ALU Control

• This material is from Chapter 4 as well as from Appendix D.
• We saw that the MIPS alu can be controled by four input lines

  ALU Control	Function
  0000	And
  0001	Or
  0010	add
  0110	subtract
  0111	slt
  1100	nor

• This is only part of the instuction set, but will do for our example.
• The control unit will send the following signals to the ALU control

  Opcode	ALUOP
  LW/SW	00
  Beq	01
  R-TYPE	10

  • Do LW and SW need the same computation?
  • Are all R-type instructions created equal?
  • How can we tell R-type instructions apart?
• They build the following table, where X means "don't care"

• Instruction	ALUOp	FNCTL	ALU Action	ALU Control
  LW/SW	00	-	add	0010
  BEQ	01	-	subtract	0110
  add	10	10 0000	add	0010
  subtract	10	10 0010	subtract	0110
  AND	10	10 0100	and	0000
  OR	10	10 0101	or	0001
  SLT	10	10 1010	slt (subtract+)	0111

• Notice
  • The first two bits for fnctl don't matter. They are always 10
• So the table can be simplified

  ALUOp1	ALOOp0	F3	F2	F1	F0	Operation
  0	0	X	X	X	X	0010
  0	1	X	X	X	X	0110
  1	X	0	0	0	0	0010
  1	X	0	0	1	0	0110
  1	X	0	1	0	0	0000
  1	X	0	1	0	1	0001
  1	X	1	0	1	0	0111

• They note, that many other combinations are possible, but we don't care as they are not valid.
• As we add more instructions we will have to extend the following.
• But look at bit 0 of the Operation.
  • It is only 1 when ALUOp1 is a 1 and either F0 or F3 are a 1.
  • Or O₀ = (F0+F3)ALUOp1
• Bit 1: not F2 or not ALUOp1
• Bit 2: F1 and ALUOp1 or ALUOp0
• Bit 3 is always 0.
• So they provide the following circuit