Digital Logic and Transistors The invention of the transistor made - - PowerPoint PPT Presentation

▶

Feb 05, 2024 251 likes •495 views

Digital Logic and Transistors The invention of the transistor made binary logic the cheapest and most effective way to implement logic gates. Both inputs are on. At least one input is on. The input is off. What is an

SLIDE 1

Digital Logic and Transistors

The invention of the transistor made binary logic the cheapest and most effective way to implement logic gates. Both inputs are “on”. At least one input is “on”. The input is “off”.

SLIDE 2

SLIDE 3

What is an “Instruction”?

Let’s consider the simple operation of adding two numbers. Adder

add x, y, z

01010010010 11100100011 Why are numbers represented in binary? How would we add binary numbers?

SLIDE 4

Adding on a CPU

Adder

Every instruction in a CPU is composed of logic gates. With current technology, gates are about 200 nm - roughly 300 times smaller than the diameter of a human hair.

x y z

SLIDE 5

Circuits and Boolean Logic

0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 0 1-bit numbers 2-bit numbers 00 + 00 = 00 00 + 01 = 01 00 + 11 = 11 01 + 00 = 01 ... How many entries? How many possible sums can two n-bit numbers have? What does an adding circuit look like? Let’s consider adding in binary: 1

carry

input

utput

SLIDE 6

Circuits and Boolean Logic

0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 0 1-bit numbers What does an adding circuit look like? Let’s consider adding in binary: 1

carry

x y 0 1 1 0 1 1 0 0 Adder c z 1 1 1

input

utput

input

carry

utput

SLIDE 7

Circuits and Boolean Logic

0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 0 1-bit numbers What does an adding circuit look like? Let’s consider adding in binary: 1

carry

x y 0 1 1 0 1 1 0 0 Adder

input

utput

input

c z 1 1 1

carry

utput

SLIDE 8

Circuits and Boolean Logic

0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 0 1-bit numbers What does an adding circuit look like? Let’s consider adding in binary: 1

carry

x y 0 1 1 0 1 1 0 0

input

utput

input

c z 1 1 1

carry

utput

Can we calculate z and c using logic gates?

? c = z = ?

SLIDE 9

Circuits and Boolean Logic

0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 0 1-bit numbers What does an adding circuit look like? Let’s consider adding in binary: 1

carry

x y 0 1 1 0 1 1 0 0

input

utput

input

c z 1 1 1

carry

utput

Can we calculate z and c using logic gates?

? c = z = x  y

SLIDE 10

Circuits and Boolean Logic

0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 0 1-bit numbers What does an adding circuit look like? Let’s consider adding in binary: 1

carry

x y 0 1 1 0 1 1 0 0

input

utput

input

c z 1 1 1

carry

utput

c = z =

Can we calculate z and c using logic gates?

x  y x  y = (xy)  (xy)

SLIDE 11

Circuits and Boolean Logic

What does an adding circuit look like? Let’s consider adding in binary: A one-bit adder needs 4 gates. How do we add numbers with more bits?

z = (xy)  (xy) c = x  y x y c z

0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 0 1-bit numbers 1

carry

input

utput

SLIDE 12

Adder Logic

We need to modify our 1-bit adder slightly to use it in series: 01010010010 11100100011

x y z c

SLIDE 13

Adder Logic

We need to modify our 1-bit adder slightly to use it in series: 1 01010010010 11100100011 00

x y z c

SLIDE 14

Adder Logic

We need to modify our 1-bit adder slightly to use it in series: 01 01010010010 11100100011 100

x y z c

SLIDE 15

Adder Logic

We need to modify our 1-bit adder slightly to use it in series: 101 01010010010 11100100011 0100

x y z c

SLIDE 16

Adder Logic

We need to modify our 1-bit adder slightly to use it in series: 0101 01010010010 11100100011 00100

x y z c

SLIDE 17

Adder Logic

We need to modify our 1-bit adder slightly to use it in series: 10101 01010010010 11100100011 000100

x y z c

SLIDE 18

Adder Logic

We need to modify our 1-bit adder slightly to use it in series: 110101 01010010010 11100100011 0000100

x y z c

SLIDE 19

Adder Logic

We need to modify our 1-bit adder slightly to use it in series: 0110101 01010010010 11100100011 00000100

x y z c

SLIDE 20

Adder Logic

We need to modify our 1-bit adder slightly to use it in series: 10110101 01010010010 11100100011 000000100

x y z c

SLIDE 21

Adder Logic

We need to modify our 1-bit adder slightly to use it in series: 110110101 01010010010 11100100011 0000000100

x y z c

SLIDE 22

Adder Logic

We need to modify our 1-bit adder slightly to use it in series: 0110110101 01010010010 11100100011 10000000100

x y z c

SLIDE 23

Adder Logic

We need to modify our 1-bit adder slightly to use it in series: 100110110101 01010010010 11100100011 10000000100

x y z c

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

x y z cin cout

SLIDE 24