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Constructing Computer - Computer Organization and Design - Lecture Slides, Slides of Computer Aided Design (CAD)

Baba Ghulam Shah Badhshah University Computer Aided Design (CAD)

The digital system design, is very helpful series of lecture slides, which made programming an easy task. The major points in these laboratory assignment are:Constructing Computer, Gate-Level, Useful Logic Circuits, Arithmetic-Logic Unit, Multiplexors, Registers, Memories, State Element, Positive Edge-Triggered Flip-Flop, Positive Edge of Clock, Combinational Logic

Typology: Slides

2012/2013

Uploaded on 04/24/2013

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Constructing a Computer

•Creating a general purpose computing device involves

a lot of logic

•Putting together an entire processor at the gate-level

isn’t very feasible

•For the next set of classes, we’ll put together a toolbox

of useful logic circuits that we can use in our processor:

–Multiplexors

–Arithmetic-Logic Unit ( ALU )

–Registers

–Memories

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Discover Slides of Computer Aided Design (CAD) Baba Ghulam Shah Badhshah University

Partial preview of the text

Download Constructing Computer - Computer Organization and Design - Lecture Slides and more Slides Computer Aided Design (CAD) in PDF only on Docsity!

Constructing a Computer

• Creating a general purpose computing device involves

a lot of logic

• Putting together an entire processor at the gate-level

isn’t very feasible

• For the next set of classes, we’ll put together a toolbox

of useful logic circuits that we can use in our processor:

Multiplexors
Arithmetic-Logic Unit ( ALU )
Registers
Memories

State Logic – D Flip-Flop

• A state element that is edge-sensitive

– Want changes in output ONLY on the transition of the Clk signal

from 0  1 (or from 1  0)

D Q

Q

positive edge-triggered flip-flop

Combinational Logic

• Changes in input values are reflected immediately (subject

to the speed of light and electrical delays) on the outputs

• Each gate has an associated “electrical delay”

• Delays are often ignored for the purpose of the logic

design (but not for the real implementation!)

• As soon as inputs change, the outputs change – no

memory of what happened before

(at least conceptually)

Converting Boolean Algebra into Gates

C = SA + SB
What does this device do?
A steering device: S steers/switches A or B onto the output C

A

B

C

1-Bit ALU

• ALU = Arithmetic Logic Unit

A combinational logic device that performs arithmetic and logic operations on a set of inputs (in most cases, 2)
Not clocked – slowed only by electrical delays (combinational logic)

• For example, if we require 4 operations:

1-Bit ALU (AND and OR)

• AND an OR are simple to implement!

• Need 1 bit of control to select

between the two operations

1 Bit Binary Addition

– The combinational logic for Sum (S) is

or

– The combinational logic for Carry out (C) is

– These two portions together is called a “half-adder”:

A

S

AB S

AB C

AB HA CS

Hypothetical

• How would I add together two 4-bit numbers?

• String them together

– Need some mechanism for carries

1 Bit Binary Addition

• S = Cin A B + Cin A B + Cin A B + Cin A B

= Cin(A B + A B) + Cin (A B + A B)

= Cin (A  B) + Cin (A  B)

= Cin  (A  B)

= Cin  A  B

• Cout = Cin A B + Cin A B + Cin A B + Cin A B

= A B + B Cin + A Cin (the “majority”

function)

1 Bit Binary Addition

The combinational logic for Sum (S) is
The combinational logic for Carry Out (C) is
The result is called a “full-adder”:

CinAB FA CoutS

S

AB

Cin

Detecting Overflow

Overflow = Cin  Cout of the full adder corresponding to the MSB

A0 FA

B

S

Cout

Cin

FA

A

B1 Cout S

Cin

FA

A

B2 Cout S

Cin

A3 FA

B

S

Cout

Cin

Overflow

4-Bit Subtraction

Computing C = A - B where A, B, and C are all 4-bit values
Note: C = A + (B + 1)
Inputs need to be A and B
LSB Cin  1

FA

A

B0' Cout S

Cin

A1 FA

B1'

S

Cout

Cin

A2 FA

B2'

S

Cout

Cin

FA

A

B3' Cout S

Cin

Overflow

4x1 MUX

A 4x1 MUX provides for 4 1-bit inputs (A,B,C,D) and a single 1-bit output
4 inputs requires 2 select bits (S1 and S0)
S1:S0 steer one of four inputs onto a single 1-bit output line
Function table: (^) S1 S0 Output

0 0 A

0 1 B

1 0 C

1 1 D

A

C Output

B

D

S1 S

Design of a 1-Bit ALU

Requires:
- 4x1 MUX
- 2x1 MUX
- 1 FA
- 1 AND
- 1 OR
- 1 NOT

FA

A

B

Cin C1 C

Cout

C

4x1 MUX

Constructing Computer - Computer Organization and Design - Lecture Slides, Slides of Computer Aided Design (CAD)

Related documents

Partial preview of the text

Download Constructing Computer - Computer Organization and Design - Lecture Slides and more Slides Computer Aided Design (CAD) in PDF only on Docsity!

Constructing a Computer

• Creating a general purpose computing device involves

a lot of logic

• Putting together an entire processor at the gate-level

isn’t very feasible

• For the next set of classes, we’ll put together a toolbox

of useful logic circuits that we can use in our processor:

State Logic – D Flip-Flop

• A state element that is edge-sensitive

– Want changes in output ONLY on the transition of the Clk signal

from 0  1 (or from 1  0)

D Q

Q

positive edge-triggered flip-flop

Combinational Logic

• Changes in input values are reflected immediately (subject

to the speed of light and electrical delays) on the outputs

• Each gate has an associated “electrical delay”

• Delays are often ignored for the purpose of the logic

design (but not for the real implementation!)

• As soon as inputs change, the outputs change – no

memory of what happened before

A

B

C

1-Bit ALU

• ALU = Arithmetic Logic Unit

• For example, if we require 4 operations:

1-Bit ALU (AND and OR)

• AND an OR are simple to implement!

• Need 1 bit of control to select

between the two operations

1 Bit Binary Addition

– The combinational logic for Sum (S) is

or

– The combinational logic for Carry out (C) is

– These two portions together is called a “half-adder”:

A

S

AB S

AB C

AB HA CS

Hypothetical

• How would I add together two 4-bit numbers?

• String them together

– Need some mechanism for carries

1 Bit Binary Addition

• S = Cin A B + Cin A B + Cin A B + Cin A B

= Cin(A B + A B) + Cin (A B + A B)

= Cin (A  B) + Cin (A  B)

= Cin  (A  B)

= Cin  A  B

• Cout = Cin A B + Cin A B + Cin A B + Cin A B

= A B + B Cin + A Cin (the “majority”

function)

1 Bit Binary Addition

S

AB

Detecting Overflow

A0 FA

B

S

FA

A

FA

A

A3 FA

B

S

4-Bit Subtraction

FA

A

A1 FA

B1'

S

A2 FA