how computers compute

How Computers Compute

(6+2*3)/22–6/3

How we humans compute?

(6+2*3)/22–6/3


Operator Precedence:

3: POW (^)

2: MUL, DIV (*, /)

1: ADD, SUB (+,-)

0: Parenthesis

(6+2*3)/22–6/3


3: POW (̂ )

2: MUL, DIV (*, /)

1: ADD, SUB (+,-)

0: Parenthesis

(6+2*3)/22–6/3

(6+2*3)/4–6/3


3: POW (̂ )

2: MUL, DIV (*, /)

1: ADD, SUB (+,-)

0: Parenthesis

(6+2*3)/22–6/3

(6+2*3)/4–6/3

(6+6)/4–6/3


3: POW (̂ )

2: MUL, DIV (*, /)

1: ADD, SUB (+,-)

0: Parenthesis

(6+2*3)/22–6/3

(6+2*3)/4–6/3

(6+6)/4–6/3

(6+6)/4–2


3: POW (̂ )

2: MUL, DIV (*, /)

1: ADD, SUB (+,-)

0: Parenthesis

(6+2*3)/22–6/3

(6+2*3)/4–6/3

(6+6)/4–6/3

(6+6)/4–2

12/4–2


3: POW (̂ )

2: MUL, DIV (*, /)

1: ADD, SUB (+,-)

0: Parenthesis

(6+2*3)/22–6/3

(6+2*3)/4–6/3

(6+6)/4–6/3

(6+6)/4–2

12/4–2

3–2


3: POW (̂ )

2: MUL, DIV (*, /)

1: ADD, SUB (+,-)

0: Parenthesis

(6+2*3)/22–6/3

(6+2*3)/4–6/3

(6+6)/4–6/3

(6+6)/4–2

12/4–2

3–2

1


3: POW (̂ )

2: MUL, DIV (*, /)

1: ADD, SUB (+,-)

0: Parenthesis

CPU

Memory

Program

VS

CPU

Memory

Program

This is actually pretty stupid

VS

● Get data from program/memory● Push data to memory

CPU

Memory

Program

What a CPU can do?

● Get data from program/memory● Push data to memory● Perform operations with data from memory

AdditionSubtractionMultiplicationDivision

CPU

Memory

Program

What a CPU can do?



CPU

Memory

Program

What a CPU can do?

“Variations” of Addition (Binary format perk)



CPU

Memory

Program

What a CPU can do?

“Variations” of Addition (Binary format perk)

RISC Reduced Instruction Set Computing

CPU

Memory

Program

(6+2*3)/22–6/3

This should go there...

Running a program

CPU

Memory

Program

(6+2*3)/22–6/3

But the CPU won’t understand this program!!!

Running a program

(6+2*3)/22–6/3

(6+2*3)/4–6/3

(6+6)/4–6/3

(6+6)/4–2

12/4–2

3–2

1

Let’s flip our previous pyramid

1

3–2

12/4–2

(6+6)/4–2

(6+6)/4–6/3

(6+2*3)/4–6/3(6+2*3)/22–6/3

Let’s flip our previous pyramid

1

3–2

12/4–2

(6+6)/4–2

(6+6)/4–6/3

(6+2*3)/4–6/3(6+2*3)/22–6/3

And create a Graph with the steps taken

1

3–2

12/4–2

(6+6)/4–2

(6+6)/4–6/3

(6+2*3)/4–6/3(6+2*3)/22–6/3


-

1

3–2

12/4–2

(6+6)/4–2

(6+6)/4–6/3

(6+2*3)/4–6/3(6+2*3)/22–6/3


-

/

1

3–2

12/4–2

(6+6)/4–2

(6+6)/4–6/3

(6+2*3)/4–6/3(6+2*3)/22–6/3


-

/

+

1

3–2

12/4–2

(6+6)/4–2

(6+6)/4–6/3

(6+2*3)/4–6/3(6+2*3)/22–6/3


-

/

+/

1

3–2

12/4–2

(6+6)/4–2

(6+6)/4–6/3

(6+2*3)/4–6/3(6+2*3)/22–6/3


-

/

+/

*

1

3–2

12/4–2

(6+6)/4–2

(6+6)/4–6/3

(6+2*3)/4–6/3(6+2*3)/22–6/3


-

/

+/

* ^

1

3–2

12/4–2

(6+6)/4–2

(6+6)/4–6/3

(6+2*3)/4–6/3(6+2*3)/22–6/3


-

/

+/

* ^6

2 3 2 2

6 3

Let’s apply a Post-order Traversal

-

/

+/

* ^6

2 3 2 2

6 3

Algorithm:

Resolve left subtree

Resolve right subtree

Resolve node

Let’s apply a Post-order Traversal

-

/

+/

* ^6

2 3 2 2

6 3

Algorithm:



Resolve node

623*+22^/63/-

Let’s apply an Post-order Traversal

-

/

+/

* ^6

2 3 2 2

6 3

Algorithm:



Resolve node

this is what compilers do!

From: (6+2*3)/22–6/3To: 623*+22^/63/-

Abstract Syntax Tree (AST)

CPU -/36/^22+*32 6

Memory

623*+22^/63/-

reversed

Random Fact: HP48 calculators work with postfix notation only

CPU -/36/^22+*32 6

CPU -/36/^22+*3 2

6

CPU -/36/^22+* 3

62

CPU -/36/^22+ *

62

3

Take 2 items from memory, multiply them and leave the

result in memory

CPU -/36/^22 +

6 6

Take 2 items from memory, multiply them and leave the

result in memory

CPU -/36/^2 2

12

CPU -/36/^ 2

12

2

CPU -/36/ ^

12

22

CPU -/36 /

12

4

CPU -/3 6

3

CPU -/ 3

36

CPU- /

363

CPU-

32

CPU

1

End!Q&A

how computers compute

Technology