flowcharts, modularity, and numbers
inf1339
faculty of information
university of toronto

https://www.youtube.com/playlist?list=PLOeQ9PMoKtR7be4eT6QtwfGkthrdqhuUr

Outcomes

  • Pseudocode2Flowchart
  • Flowchart2Pseudocode
  • Real World ↔ Pseudocode ↔ Flowchart
  • Critique and Fix Ill-formed flowcharts
  • Flowcharts and stepwise refinement
  • Flowcharts and black boxes
  • Flowcharts and modularity
  • Binary numbers
    • count by 2, powers of 2, bin2dec, dec2bin
  • Hexadecimal numbers
    • count by x, bin2hex, hex2bin, hex2dec, dec2hex

NOTES

Review Questions

Review Qs FLOW | Review Qs NUMBERS

Crowd Sourced Notes

Tutorial

Problem Sets

 Image from "Healers of the Wild: People Who Care for Injured and Orphaned Wildlife" by Shannon K. Jacobs, by way of the Wild Bird Fund. 

Flowchart = visualization of sequence and contingency

WHAT FLOWS?

A TO DO List is not an agenda!

Contingency

Wake Up

Shower

Eat

Read

M,W,F

Shake

Egg


Make Breakfast
 

Wake Up

Shower

Eat

Read

M,W,F

Shake

Egg


Make Breakfast
 

Wake Up

Shower

Eat

Read

M,W,F

Shake

Egg


Make Breakfast
 

Wake Up

Shower

Eat

Read

Make Breakfast

M,W,F

Shake

Egg

Wake Up

Shower

Eat

Read

Make Breakfast

M,W,F

Shake

Egg

Wake Up

Shower

Eat

Read

M,W,F

Shake

Egg


Make Breakfast
 

FLOWCHART CONVENTIONS

The Elements of Flow(charts)

arrow

flow

"go to..."

circle

terminal/connector

"and then..."

diamond

decision/branch

"if this is true..."

rectangle

module/action

"do this"

Flow in and Flow Out

Control flows INTO THE TOP and OUT OF THE BOTTOM of rectangles.

Control flows INTO THE TOP and OUT THE SIDES of diamonds.

Control can flow INTO THE TOP, IN FROM THE LEFT, or both IN  FROM and OUT TO THE SIDES of a connector circle.

\

O

\

O

\

O

Grammar of Flowcharts

Entry Circle

Exit Circle

Zero or

more

MODULES

module

But what is a module?

Module

action

module

condition

module

condition

module

condition

module

OR

OR

OR

OR

module

action

action

action

action

module

action

action

action

action

module

module

condition

module

condition

module

module

condition

module

condition

module

condition

module

module

condition

module

module

module

condition

module

module

condition

module

condition

module

module

condition

module

condition

module

condition

RULE: Every Module has a Single Entry and a Single Exit

This can be a single action or any combination of sequence and contingency.

MODULE: any chunk of activity that can be popped into or out of a flowchart because of its single entry single exit property.

MODULE

How Does "Single Entry Single Exit" Rule Apply to Decisions?

Diamonds Do Not Stand Alone

condition
A

do action
B

do action
C

if condition A
     do action B
else
     do action C

the diamond splits the

flow into branches

the circle rejoins the

branches into a single exit

Diamond = IF-THEN-ELSE Module

condition
A

do action
B

do action
C

if condition A
     do action B
else
     do action C

Diamond = IF-THEN-ELSE Module

condition
A

do action
B

do action
C

if condition A
     do action B
else
     do action C

Two Special "if-then-else" Modules

While it is raining, keep your umbrella up.

Keep your umbrella up until it stops raining.

"if-then-else" > WHILE Modules

While it is raining, use an umbrella.

If it is raining, use an umbrella, if not, put the umbrella away. Check every few minutes to see if it is still raining.

Is it raining?

    Yes? Use an umbrella

    Check again

Put the umbrella away

raining?

use umbrella

put umbrella away

New Concept: Flowchart for Repetition

WHILE A DO B

A?

B

YES

NO

SINGLE EXIT POINT

SINGLE ENTRY POINT

"if-then-else" > UNTIL Modules

Use an umbrella. Check every few minutes to see if it is still raining.  When it stops, put the umbrella away.

Use an umbrella

    Check for rain

    If no rain, proceed.

Put the umbrella away

use umbrella

put umbrella away

Keep your umbrella up until it stops raining.

stopped raining?

New Concept: Flowchart for Repetition

REPEAT B UNTIL A

A?

B

SINGLE EXIT POINT

SINGLE ENTRY POINT

NO

YES

In a WHILE loop, the "action" may be executed ZERO OR MORE TIMES

In an UNTIL loop, the "action" is always executed AT LEAST ONCE (i.e., "one or more times")

Practice

Example 1

If today is Tuesday, we must be in Belgium

Tuesday?

Belgium

YES

?

Example 2

DO A. 
IF B, 
   DO C, 
   otherwise DO D. 
DO E. 
DO F.

B

A

E

F

C

D

YES

NO

IF B

DO C

OTHERWISE D

IF B, 
   DO C, 
   otherwise DO D.

Example 2

DO A. 
IF B, 
   DO C, 
   otherwise DO D. 
DO E. 
DO F.

B

A

E

F

C

D

YES

NO

IF B

DO C

OTHERWISE D

IF B, 
   DO C, 
   otherwise DO D.

How to find wildlife rehab

hurt or sick?

feathered?

nestling

intact?

see nest?

safe?

put in nest

parents?

make nest

put in nest

parents?

leave

leave

put in bushes

parents?

leave

wildlife rehab

wildlife rehab

leave

wildlife rehab

fledgling

Y

Y

Y

Y

Y

Y

Y

Y

Q: How would you redraw this flowchart in "standard" form?

How to find wildlife rehab

hurt or sick?

feathered?

nestling

intact?

see nest?

safe?

put in nest

parents?

make nest

put in nest

parents?

leave

leave

put in bushes

parents?

leave

wildlife rehab

wildlife rehab

leave

wildlife rehab

fledgling

Y

Y

Y

Y

Y

Y

Y

Y

How to find wildlife rehab

hurt or sick?

feathered?

nestling

intact?

see nest?

safe?

put in nest

parents?

make nest

put in nest

parents?

leave

leave

put in bushes

parents?

leave

wildlife rehab

wildlife rehab

leave

wildlife rehab

fledgling

Y

Y

Y

Y

Y

Y

Y

Y

How to find wildlife rehab

hurt or sick?

feathered?

nestling

intact?

see nest?

safe?

put in nest

parents?

make nest

put in nest

parents?

leave

leave

put in bushes

parents?

leave

wildlife rehab

wildlife rehab

leave

wildlife rehab

fledgling

Y

Y

Y

Y

Y

Y

Y

How to find wildlife rehab

hurt or sick?

feathered?

nestling

intact?

see nest?

safe?

put in nest

parents?

make nest

put in nest

parents?

leave

leave

put in bushes

parents?

leave

wildlife rehab

wildlife rehab

leave

wildlife rehab

fledgling

Y

Y

Y

Y

Y

Y

Y

hurt or sick?

feathered?

nestling

intact?

see nest?

safe?

put in nest

parents?

make nest

put in nest

parents?

leave

leave

put in bushes

parents?

leave

wildlife rehab

wildlife rehab

leave

fledgling

Y

Y

Y

Y

Y

Y

Y

How to find wildlife rehab

wildlife rehab

hurt or sick?

feathered?

nestling

intact?

see nest?

safe?

put in nest

parents?

make nest

put in nest

parents?

leave

leave

put in bushes

parents?

leave

wildlife rehab

wildlife rehab

leave

fledgling

Y

Y

Y

Y

Y

Y

Y

How to find wildlife rehab

wildlife rehab

hurt or sick?

feathered?

nestling

intact?

see nest?

safe?

put in nest

parents?

make nest

put in nest

parents?

leave

leave

put in bushes

parents?

leave

wildlife rehab

wildlife rehab

leave

fledgling

Y

Y

Y

Y

Y

Y

Y

How to find wildlife rehab

wildlife rehab

hurt or sick?

feathered?

nestling

intact?

see nest?

safe?

put in nest

parents?

make nest

put in nest

parents?

leave

leave

put in bushes

parents?

leave

wildlife rehab

wildlife rehab

leave

fledgling

Y

Y

Y

Y

Y

Y

Y

wildlife rehab

How to find wildlife rehab

wildlife rehab

hurt or sick?

feathered?

nestling

intact?

see nest?

safe?

put in nest

parents?

make nest

put in nest

parents?

leave

leave

put in bushes

parents?

leave

wildlife rehab

wildlife rehab

leave

fledgling

Y

Y

Y

Y

Y

Y

Y

wildlife rehab

How to find wildlife rehab

wildlife rehab

hurt or sick?

feathered?

nestling

intact?

see nest?

safe?

put in nest

parents?

make nest

put in nest

parents?

leave

leave

put in bushes

parents?

leave

wildlife rehab

wildlife rehab

leave

fledgling

Y

Y

Y

Y

Y

Y

Y

wildlife rehab

How to find wildlife rehab

wildlife rehab

hurt or sick?

feathered?

nestling

intact?

see nest?

safe?

put in nest

parents?

make nest

put in nest

parents?

leave

leave

put in bushes

parents?

leave

wildlife rehab

wildlife rehab

leave

fledgling

Y

Y

Y

Y

Y

Y

Y

wildlife rehab

How to find wildlife rehab

wildlife rehab

hurt or sick?

feathered?

nestling

intact?

see nest?

safe?

put in nest

parents?

make nest

put in nest

parents?

leave

leave

put in bushes

parents?

leave

wildlife rehab

wildlife rehab

leave

fledgling

Y

Y

Y

Y

Y

Y

Y

wildlife rehab

How to find wildlife rehab

wildlife rehab

hurt or sick?

feathered?

nestling

intact?

see nest?

safe?

put in nest

parents?

make nest

put in nest

parents?

leave

leave

put in bushes

parents?

leave

wildlife rehab

wildlife rehab

leave

fledgling

Y

Y

Y

Y

Y

Y

Y

wildlife rehab

How to find wildlife rehab

wildlife rehab

hurt or sick?

feathered?

nestling

intact?

see nest?

safe?

put in nest

parents?

make nest

put in nest

parents?

leave

leave

put in bushes

parents?

leave

wildlife rehab

wildlife rehab

leave

fledgling

Y

Y

Y

Y

Y

Y

Y

wildlife rehab

wildlife rehab

How to find wildlife rehab

wildlife rehab

How to find wildlife rehab

hurt or sick?

feathered?

nestling

intact?

see nest?

safe?

put in nest

parents?

make nest

put in nest

parents?

leave

leave

put in bushes

parents?

leave

wildlife rehab

wildlife rehab

leave

wildlife rehab

fledgling

Y

Y

Y

Y

Y

Y

Y

wildlife rehab

wildlife rehab

Q1020.

I scored an amazing summer practicum washing pots in a restaurant. My boss is a computational thinker and wants me to post a flowchart describing the pot-washing process on the wall behind the pot-washing sinks. Here are her instructions:

Scrub until clean. Rinse until clear. Inspect. If not OK, start over.

Proceed Stepwise: (1) Pseudocode; (2) Outside; (3) Inside

Q1020.

                      I scored an amazing summer practicum washing pots in a restaurant. My boss is a computational thinker and wants me to post a flowchart describing the pot-washing process on the wall behind the pot-washing sinks. Here are her instructions:

Scrub until clean. Rinse until clear. Inspect. If not OK, start over.

Proceed Stepwise: (1) Pseudocode; (2) Outside; (3) Inside

scrub
until clean
rinse
until clear
inspect
if OK, done
else, start over
repeat
    repeat
       scrub
    until clean
    repeat
       rinse
    until clear
    inspect
until OK

Q1020.

                      I scored an amazing summer practicum washing pots in a restaurant. My boss is a computational thinker and wants me to post a flowchart describing the pot-washing process on the wall behind the pot-washing sinks. Here are her instructions:

Scrub until clean. Rinse until clear. Inspect. If not OK, start over.

Proceed Stepwise: (1) Pseudocode; (2) Outside; (3) Inside

Q1020.

                      I scored an amazing summer practicum washing pots in a restaurant. My boss is a computational thinker and wants me to post a flowchart describing the pot-washing process on the wall behind the pot-washing sinks. Here are her instructions:

Scrub until clean. Rinse until clear. Inspect. If not OK, start over.

Proceed Stepwise: (1) Pseudocode; (2) Outside; (3) Inside

What's Wrong with this Survey Question?

Q2. What is your gender?

              Female

              Male

Q2. What is your gender?

              Female

              Male

What's Wrong with this Survey Question?

Q3. Which category are you in?

              Canadian

              Student

              Climate Change Denier

              Big Fan of Teddy Bears

Exhaustive & Mutually Exclusive

Exhaustive means the given options represent all possibilities

Mutually Exclusive means the given options do not overlap

In Management and Strategy 

See, for example, "What is the MECE Principle?" at StrategyU

Exhaustive & Everything Else

action A

action B

action C

green hair/fur/feathers?

2 legs?

action A

action A

action B

action B

action C

action C

action C

Mutually Exclusive

Flowcharts describe DETERMINISTIC processes

At any decision point the condition can be evaluated and one branch or another can be chosen.

Our convention of requiring decisions to be based on  YES-NO or TRUE FALSE conditions ensures that branches are mutually exclusive.

Exhaustive and Mutually Exclusive

How to proceed at an intersection: right or left

Secret codes: if the text contains the word "bread," launch the app; if the text contains the phrase "bread and roses," don't launch the app; if the text contains the word "roses," shut the system down.

Compute X. If X is greater than 0 and less than 12, start program A; if X is greater than 10, launch program B. If X = 11, launch program C.

What to order?  If you are hungry and thirsty, order a hot dog and a beer; if you are hungry but not thirsty, order a pretzel; if you are thirsty, order a cola.

If you are over 40 you can sign up for a vaccine in May. If you are under 30 you can sign up for a vaccine in June. If you are in an at-risk category you can sign up now.

Exhaustive and Mutually Exclusive

Ordinary Deck of Cards. Choose one card at random. Which statement are exhaustive, which are muutlly exclusive?

"you chose a red card" and "you chose a black card"

"you chose a 'face' card" and "you chose an ordinary card"

"you chose a heart," "you chose a club," and "you chose a diamond"

"your card is a number card," "your card is red", "your card is clubs,"

"your card is spades"

"you chose a red card" and "you chose a seven"

EX

ME

EX

ME

EX

ME

EX

ME

EX

ME

STRETCH

NUMBERS

NUMBERS

LOGIC

condition A

condition C

condition C

condition C

condition C

S

T

U

V

W

X

Y

Z

condition B

condition B

What You Need to Know

  1. CL01 Binary: Concept of base 2; notation; count to 10; dec2bin, bin2dec; first 10 powers of 2; binary arithmetic

  2. CL02 Hexadecimal: Concept of base 16; notation; hex2bin, bin2hex, hex2dec; ASCII encoding; URL encoding; HTML color encoding

  3. CL03 Counting by Powers: exponents, graphing, logarithms

hex2bin

bin2hex

Binary = Base 2

Positional Number Systems

Positional Number Systems

Positional Number Systems

STOP+THINK

 

Count to ten in binary

0000   0001   0010   0011   0100   0101   0110   0111   1000   1001   1010

How to convert dec to bin?

Start with decimal number, "D"

Divide by 2. 
Note the result.
Write down the remainder.

Repeat process with the result.

Continue until nothing left.

D=6

divide by 2

result = 3, remainder = 0

divide by 2

result = 1, remainder = 1

divide by 2

result = 0, remainder = 1

610 = 1102

DEC2BIN Algorithm

Start with decimal number, "D"

Divide by 2. 
Note the result.
Write down the remainder.

Repeat process with the result.

Continue until nothing left.

call decimal number D

divide D by 2

write remainder R to L

replace D with result

result=0?

read remainders

STOP+THINK. Convert 123 to binary 

 123 /2 =    61 R1
  61 /2 =    30 R1
  30 /2 =    15 R0 
  15 /2 =     7 R1
   7 /2 =     3 R1
   3 /2 =     1 R1
   1 /2 =     0 R1

1

0

0

1

1

1

1

1

1

0

1

1

1

1

1

2

0

32

64

16

8

STOP+THINK. Convert 273 to binary

Solution

STOP+THINK. Convert 2421 to binary

Solution

STOP+THINK. Convert 7777 to binary

Solution

Back

7777 / 2 = 3888 R1
3888 / 2 = 1944 R0
1944 / 2 =  972 R0
 972 / 2 =  486 R0
 486 / 2 =  243 R0
 243 /2 =   121 R1
 121 /2 =    60 R1
  60 /2 =    30 R0
  30 /2 =    15 R0 
  15 /2 =     7 R1
   7 /2 =     3 R1
   3 /2 =     1 R1
   1 /2 =     0 R1

1

0

0

0

0

1

1

0

0

1

1

1

1

7777 / 2 = 3888 R1
3888 / 2 = 1944 R0
1944 / 2 =  972 R0
 972 / 2 =  486 R0
 486 / 2 =  243 R0
 243 /2 =   121 R1
 121 /2 =    60 R1
  60 /2 =    30 R0
  30 /2 =    15 R0 
  15 /2 =     7 R1
   7 /2 =     3 R1
   3 /2 =     1 R1
   1 /2 =     0 R1

1

0

0

0

0

1

1

0

0

1

1

1

1

4096 + 2048 + 1024 + 512 + 64 + 32 + 1

An earlier question asked how we might count if we had 8 fingers, four on each hand, and we came up with the idea that we would only need the digits 0, 1, 2, 3, 4, 5, 6, and 7.

STOP+THINK: But what if we had 8 fingers on EACH hand? How would we count?

When we were counting by something LESS than ten, we simply left some of the usual digits out of the picture.  If we lived in a base-8 world (where we had 8 fingers) the digits 8 and 9 would just be silly and unnecessary symbols.  If we lived in that world and wanted to think about the imaginary world in which we had ten fingers and so would count by ten we'd need two extra symbols after 7.  We could pick any at all. Maybe 0,1,2,3,4,5,6,7,X,Q,10.  

So, what if we were counting by sixteen?  Then we'd need another 6 symbols and we'd count like this

1, 2, 3, 4, 5, 6, 7, 8, 9, SYMBOL1, SYMBOL2, SYMBOL3, SYMBOL4, SYMBOL5, SYMBAL6, 10

What if we decided to use the first six letters as the symbols?  Then we'd have

1 2 3 4 5 6 7 8 9 A B C D E F 10
                  1010 1110 1210 1310 1410 1510 1610

And this is precisely how we do it in the base 16 or "HEXADECIMAL" number system. It turns out that hexadecimal is particularly useful as a counterpart to binary.  For many reasons, but one we'll start with is that the number of values that can be represented with four binary digits is sixteen (think about it: 00002 = 010, 11112 = 1510).  So, one shorthand for binary is to represent every four binary digits with a single hexadecimal digit.

Try the examples below. Match each binary number with its hexadecimal equivalent.

See Also (optional)

Other Bases

What if...

1

2

3

4

5

6

0, 1, 2, 3, 4, 5, ?

STOP+THINK. What's next?

Solution

0, 1, 2, 3, 4, 5, 10, 11, 12, 13, 14, 15, 20

STOP+THINK. What's next?

Back

More...

Base 6

Back

  64    63    62    61    60
1296  216    36     6     1
3246 =               3*36 + 2*6 + 4*1          
     =               108  + 12  + 1
     =               12110

What if...

0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,10,11,12...

0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F,10,11,12,13...

STOP+THINK. The rest of binary 0 - 15

0000 0001 0010 0011 0100 0101 0110 0111 1000 1001

1010 = 10

1011 = 11

1100 = 12

1101 = 13

1110 = 114

1111 = 15

BINARY & HEXADECIMAL

24     23     22     21     20
16     8      4      2      1
  164    163    162    161    160
65536   4096    256   16      1

BINARY & HEXADECIMAL

Binary Digits: 0,1

Hexadecimal Digits: 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F

HEX2DEC

3 x 163     +  10 x 162  +  15 x 161  + 7 x 160

3 x 4096   +  10 x 256  +  15 x 16   +   7 x 1

12288    +     2560     +      240      +      7 

15095   

3

A

F

7

STOP+THINK. HEX2DEC 

FF
111
2000
ACE
C0DE
1000
=15*16+15=25510
=256+16+1=27310
=2*4096=819210
=10*256+12*16+14
=2560+206=276610
=12*4096+13*16+14
=4937410
=409610
162=256   163=4096

Click for solutions

BIN2HEX

1011010101010111101010101010

1011   0101   0101   0111   1010   1010   1010

B        5         5          7          A          A         A

{

HEX2BIN

1011010101010111101010101010

1011   0101   0101   0111   1010   1010   1010

B        5         5          7          A          A         A

{

ENCODING

ASCII

American Standard Code for Information Interchange

  • Numerical code for letters, digits, symbols
     
  • Goes back to the days of teletype, hence the
    control character symbols such as BEL
     
  • Seven binary digits encode 128 symbols

STOP+THINK. Decode this ASCII text

Solution

4465636F 64652074
68697320 41534349
49207465 787460

Other Notations

subscripts: 15916    159hex    159h

prefix: 0x1F9

special characters in URLs as hex pairs prefixed with %

characters in XML and HTML as hex pairs with &#xcode;

colors in HTML & CSS: 3 hex pairs* (red, green and blue) prefixed with #

http://www.example.com/name%20with%20spaces
’ = character U+2019 (’).

This Orange = #FFAA33

*CSS allows 3-hex digit abbreviation, one per component: #FA3 = #FFAA33.

STOP+THINK: CSS Colors

#17e71e

#abcdef

#8800FF

Which color is

#17e71e

#abcdef

#8800FF

See also: "HTML Symbols"

STOP+THINK: HTML &codes

Text

N.B.  16110 = 0xA1

Wait, there's more...

BINARY ARITHMETIC

  • ADDING SINGLE BITS TOGETHER
  • THE CARRY BIT
  • MULTIPLYING IN BINARY

Binary
Arithmetic

 1
+1
10

Arithmetic in Binary

0 + 0 = 0

0 + 1 = 1

1 + 1 = 10

10 + 1 = 11

10 + 10 = 100

STOP+THINK
Could we write
numbers
with TimBits?

STOP+THINK
Could we do math
with TimBits?

Next: LOGIC

 1
+0
01

 0
+1
01

 0
+0
00

 1
+1
10

  A
 +B
 WX

A B  W X 
1 1  1 0
1 0  0 1
0 1  0 1
0 0  0 0