Computer Science 210 Computer Organization The Arithmetic Logic Unit

Computer Science 210Computer Organization

The

Arithmetic Logic Unit

ALU - General

• Goal is to design simple ALU

• Actually there are relatively few basic arithmetic logic operations needed

• Many instructions can be implemented in terms of the basic ones

ALU Building Blocks

AND GateNOT Gate

OR Gate Multiplexor

• Let's build an ALU to support the andi and ori instructions– we'll just build a 1 bit ALU, and use 32 of them

An ALU (arithmetic logic unit)

ba

operation

result

• Selects one of the inputs to be the output, based on a control input

• We’ll use a MUX for our ALU

Review: The Multiplexer

0

1

S

CA

B

1-Bit Logical Unit

0

1

0 - AndOperation 1 - Or

Result

Operation

1-Bit ALU with Addition

b

0

2

R e su lt

O pe ra t io n

a

1

C a rry In

C a rryO u t

32 bit ALU

b

0

2

Result

Operation

a

1

CarryIn

CarryOut

Result31a31

b31

Result0

CarryIn

a0

b0

Result1a1

b1

Result2a2

b2

Operation

ALU0

CarryIn

CarryOut

ALU1

CarryIn

CarryOut

ALU2

CarryIn

CarryOut

ALU31

CarryIn

• Two's complement approach: just negate b and add one.

• How do we negate?

What about subtraction (a – b) ?

0

2

Result

Operation

a

1

CarryIn

CarryOut

0

1

Binvert

b

32 bit ALU

Result31a31

b31

Result0

CarryIn

a0

b0

Result1a1

b1

Result2a2

b2

Operation

ALU0

CarryIn

CarryOut

ALU1

CarryIn

CarryOut

ALU2

CarryIn

CarryOut

ALU31

CarryIn

0

2

Result

Operation

a

1

CarryIn

CarryOut

0

1

b

binvert

binvert = 1, carryin = 1, operation = 2, gives a + ~b + 1 = a - b

binvert

+

Overflow Detection

Operation Operand A Operand B Result

+ 0 0 < 0

+ < 0 < 0 0

- 0 < 0 < 0

- < 0 0 0

Note: This can be determined by what happens in the high order bit.

Overflow Detection

Operation A’s High Bit B’s High Bit ResultHigh Bit

+ 0 0 1

+ 1 1 0

- 0 1 1

- 1 0 0

Note: If we used the output of the binvert MUX, the rows for subtraction would be the same as for addition.

Overflow Detection

A’s High Bit

Binvert MUX ResultHigh Bit

Overflow

0 0 1 1

1 1 0 1

Note: The other rows of a truth table for Overflow wouldbe 0. So, we could build an overflow detector with

_ _ _AMR + AMR

High Order 1-Bit ALU(with overflow hardware)

0

2

Resu lt

O peration

a

1

Carry In

CarryOut

0

1

B inve rt

b

Overflow