1 2-bits, 4-bits, 6-bits, a dollar The ripple carry adder o We have - - PDF document

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CS240 Computer Organization

Department of Computer Science Wellesley College

The CPU’s workhorse

Constructing a basic ALU

• Logical operations are

easiest, because they map directly onto the hardware.

• Of course we will need to

array this to a full 32- bits.

ALU 14-2

Starting out slow

ALU 14-3

Addition is next

a b CarryIn Sum CarryOut 1 1 1 1 1 1 1 1 1 1 1 1

ALU 14-4

CarryOut

a b CarryIn Sum CarryOut 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

*A CarryOut occurs as either as CarryGenerate + CarryProprogate.

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ALU 14-5

2-bits, 4-bits, 6-bits, a dollar

• We have a 1-bit ALU that

performs AND, OR, and addition.

• We create a full 32-bit

adder by arraying the results.

ALU 14-6

The ripple carry adder

ALU 14-7

Adding subtraction

• Subtraction is the same as adding the negative version of

an operand. This is how adders perform subtraction and why twos-complement is so very nice.

ALU 14-8

NOR and NAND

• A MIPS ALU also needs a NOR function. We implement

this by noting that (a + b) = a b.

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ALU 14-9

We’re getting there . . .

• . . . but we’re not home

yet.

• One instruction that still

needs support is the set

• n less than (slt)

instruction which produces 1 if a < b.

• We start by expanding

the input to the mux for Less.

ALU 14-10

Top 1-bit ALU

ALU 14-11

32-bit ALU

(Illustrates what we do with that blasted Set out and how the Less values get set.)

ALU 14-12

Finally

(Adds support for MIPS branch if equal and branch if not equal by testing whether result of

• peration equals

zero.)

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ALU 14-13

Black box representing ALU

ALU 14-14

Carry lookahead

• Carry generate

gi = ai bi.

• Carry propagate

pi = ai + bi.

• Using these define

ci+1 = gi + pi (ci).

• Now unwind the

recursion to get a sequence of equations

• nly four gates deep.