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ALU & CPUALU & CPUALU & CPUALU & CPU
Computer ArchitectureComputer Architecture
Introducing ALU
• ALU: Arithmetic & Logic Unit– Performs arithmetic operations
• Addition• Subtraction
– Performs logic operations• AND: A•B• OR: A+B• NOT: A
– Desired operation/result is chosen based on a selection logic.
Exercise
• Develop a circuit that accepts 3 inputs (say A, B, and Cin) and generates 2 outputs (say Out and Cout) depending on 3 control inputs S1,S2, and S3 as shown in the truth table:
S0 S1 S2 Out Cout0 0 0 A•B X
0 0 1 A+B X
0 1 0 A X
0 1 1 B X
1 0 0 AB Cin
AB+BCin+
ACin
X = Don’t care (can be 1 or 0)
Solution: 1-bit ALU
AB
Out
000
001
010
011
100
S0
S1
S2
S0S1S2A•B
A+B
A
B
Full AdderCinSum
Cout
Mul
tiple
xer
This approach can be extended to include other operations such as subtraction.
n-bit ALU
• n-bit ALU – Repeat 1-bit ALU n times– All 1-bit ALUs get the same selection lines
– Carry out (Cout)from one stage is wired to carry-in of next state
• Similar to how a ripple carry adder (or subtraction circuit) is wired
– Performs operation on n-bits simultaneously
Example 4-bit ALU
ALU3 ALU2 ALU1 ALU0
A3 B3 A2 B2 A1 B1 A0 B0
Add/SubO0O1O2O3O4
OP0OP1
OP2
Selection lines simply renamed to operation code (OPCode) lines
Cin Cin Cin Cin
ALU Notation• An ALU is denoted using the following graphical
notation.
ALU
Operand1 (A)
Operand2(B)
Result
8 8
9
Operation Selection
(OP Code)
Indicates number of bits on each line. The size of each
operand is typically the same and
corresponds to the word size.
4
OP Code Result
010 A•B
110 A+B
210 A
310 B
… …
Thought Experiment
• Where do the inputs to the ALU come from?– The two operands– The operation the ALU needs to perform
• Similarly where do the outputs from the ALU go?
• Solution: Registers!– The fundamental storage units.
• Fixed number of D-Flip Flops to form a Word– Corresponding to size of ALU operands!– Operate as a single unit
• Store/Read n-bits at a time
D Q
CK
D Q
CK
D Q
CK
D Q
CK
D0 D1 D2 D3
Q3Q2
Q1Q0
Registers Revisited
Selecting a Register
• Given n Registers how to read data from a specific register?
Register 1 008
Register 2 018
Register 3 108
Register 4 118
2
MUX
Register Select
8
Set of registers is called a Register File
This is not a single Mux but a set of 8 Mux’s all having the same selection logic!
Selecting 2 Registers
• ALU needs 2 operands to work!– How to select 2 registers from a Register File?
008
01
10
11
2
MUX1
Register Select 1
8
8
8
8
00
01
10
11
2
MUX2
Register Select 2
8
8
8
8
8
Register
File
Operand1 Operand2
ALU with Inputs
ALU
8 8
8
Operation
4Mux1
Mux2
Register
File
(4)
8
Operand1
2
Operand2
2
Results
What do we do with results or output from the
ALU?
ALU Output
• Solution: Put it into a register!
• OK, so do we do that?– That is, Given 1 input how to route it on n
different paths?
8
8
8
8
8
Result from ALU
Select Inputs2
DeM
ux
00
01
10
11
Register 1
Register 2
Register 3
Register 4
Handling ALU Output
ALU
8 8
8
Operation
4
Mux1
Mux2
Register
File
(4)
Flags
DeMux
8
8
8
8
8
Operand1
2
Operand2
2
Destination
2
A
B
Each device has its own slection logic typically specified using a truth
table!
Operation Result
010 A•B
110 A+B
210 A
Clock
Data path
• The ALU and associated components constitute the Data Path– Includes Registers, Multiplexers and any other
device associated with ALU operations– All operands are typically the same size
• Register sizes match with size of operand
– Size of operands are associated with CPU• 32-bit processor (ALU uses 32-bit operands) • 64-bit processor (ALU uses 64-bit operands)
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