Hexidecimal, CPU, and the Toy Computer (Week 4)

Question 1

Definition : Byte

Answer 1

A byte is a sequence of 8 bits

It encodes 256 distinct values (0 to 255)

Each distinct value represents a unique sequence of 8 bits

Question 2

Definition : Hexidecimal Numbers

Answer 2

Hexadecimal numbers use 16 symbols per digit: numerals 0-9 and letters A-F (base-16).

Question 3

Why use hexadecimal?

Answer 3

Because binary numbers rapidly grow too large to be read effectively by humans, e.g. 2021(decimal) equals 111 1110 01012(binary)

To represent binary numbers in a compact format, hexadecimal numbers are particularly suitable

Question 4

How many bits is one Hexidecimal digit?

Answer 4

1 hexadecimal digit represents exactly 4 binary digits (no more, no less)

Question 5

Convert Hexidecimal to Decimal :
A

Answer 5

10

Question 6

Convert Hexidecimal to Decimal :
B

Answer 6

11

Question 7

Convert Hexidecimal to Decimal :
C

Answer 7

12

Question 8

Convert Hexidecimal to Decimal :
D

Answer 8

13

Question 9

Convert Hexidecimal to Decimal :
E

Answer 9

14

Question 10

Convert Hexidecimal to Decimal :
F

Answer 10

15

Question 11

Convert Hexidecimal Digits to Bits :
1

Answer 11

0001

Question 12

Convert Hexidecimal Digits to Bits :
7

Answer 12

0111

Question 13

Convert Hexidecimal Digits to Bits :
3B

Answer 13

00111011

Question 14

Convert Hexidecimal to Decimal :
4B

Answer 14

75

Question 15

Convert Hexidecimal to Decimal :
A7

Answer 15

167

Question 16

Convert Hexidecimal to Decimal :
FF

Answer 16

255

Question 17

Convert Hexidecimal to Decimal :
EC

Answer 17

236

Question 18

How is color encoded?

Answer 18

In Hexidecimal eg.
ffffff
000000
00ff00

Question 19

How many bits are 7 bytes?

Answer 19

56

Question 20

What does a CPU do?

Answer 20

The CPU controls all other parts of a computer (by sending out signals on the bus)

Examples of what CPU controls: RAM, storage devices and peripherals (e.g. mouse, printer, etc.)

Question 21

What can a CPU do?

Answer 21

CPUs can execute only up to a few dozen (sometimes up to a few hundred) of quite basic instructions

1. Arithmetic: add, subtract, multiply, divide, etc. different types of numbers
2. Move data around (fetch instructions and data from RAM, store results back in RAM, move date from and to Input/Output devices)
3. Instructions to control the flow of execution, i.e. instructions that decide what to do next based on previous computation results

Question 22

What is the CPU instruction cycle?

Answer 22

CPUs perform billions of operations per second (e.g. 3 billion per second if your CPU runs at 3 GHz clock speed)

An instruction cycle features the following (simplified and) ever repeating steps:
1. Clock cycle 1: Fetch next instruction from RAM
2. Clock cycle 2: Decode what to do
3. Clock cycle 3: Execute it

Question 23

What is a Toy Computer?

Answer 23

The toy computer is a tool to simulate a highly simplified Computer/CPU in order to demonstrate how it works in principle.

It can run simple computer programs made of very basic instructions (similar to instructions of real CPUs).

The “Toy” uses one accumulator => storage area inside the CPU with capacity of one data item

Question 24

Process of the Toy Computer?

Answer 24

Programs are stored in RAM
* Each line represents one memory location
* Each location stores an instruction or data item

The CPU executes one instruction after another starting at the top.

Question 25

What do the following commands do? GET PRINT STOP

Answer 25

Answer : GET get a number from keyboard into accumulator PRINT print contents of accumulator STOP stop running

Question 26

What do the following commands do? LOAD Val STORE M ADD Val SUB Val M Num

Answer 26

Answer : LOAD Val load accumulator with Val (Val unchanged) STORE M store contents of accumulator into memory location called M (accumulator unchanged) ADD Val add Val to contents of accumulator (Val unchanged) SUB Val subtract Val from contents of accumulator (Val unchanged) M Num before program runs, set this memory location (called M) to numeric value Num

Question 27

What do the following commands do? GOTO L IFPOS L IFZERO L

Answer 27

Answer : GOTO L go to instruction labeled L IFPOS L go to instruction labeled L if accumulator is >= zero IFZERO L go to instruction labeled L if accumulator is zero

Question 28

Determine the Output of the following Toy Computer code : 1 GET (3) 2 PRINT 3 END

Answer 28

Output : error: invalid instruction 'end' at line 3

Question 29

Determine the Output of the following Toy Computer code : 1 GET (3) 2 PRINT 3 STOP

Answer 29

Output : 3

Question 30

Determine the Output of the following Toy Computer code : 1 Top GET (7, 9, 2, 0) 2 PRINT 3 GOTO Top 4 IFZERO End 5 End STOP

Answer 30

Output : error: infinite loop

Question 31

Determine the Output of the following Toy Computer code : 1 Top GET (3, 7, 0) 2 IFZERO Bot 3 ADD sum 4 STORE sum 5 GOTO Top 6 Bot LOAD sum 7 PRINT 8 STOP 9 sum

Answer 31

Output : 10

Question 32

Determine the Output of the following Toy Computer code : 1 Top GET (3, 7, 0) 2 IFZERO Bot 3 ADD sum 4 STORE sum 5 GOTO Top 6 Bot LOAD sum 7 PRINT 8 STOP

Answer 32

Output : line 3 error: there is no instruction labeled sum line 4 error: there is no instruction labeled sum line 3 error: there is no instruction labeled sum line 4 error: there is no instruction labeled sum line 6 error: there is no instruction labeled sum

Question 33

Determine the Output of the following Toy Computer code : 1 Top GET (0, 3, 7) 2 IFZERO Bot 3 ADD sum 4 STORE sum 5 GOTO Top 6 Bot LOAD sum 7 PRINT 8 STOP 9 sum

Answer 33

Output : 0

Question 34

What value(s) of GET would cause an error? 1 GET 2 Loop Sub 1 3 PRINT 4 IFZERO Exit 5 GOTO Loop 6 Exit STOP

Answer 34

If 0 or less (0,-1,-2, -3, ...) is the input, the program will loop infinitely. error: infinite loop

Question 35

What value(s) of GET would cause an error? 1 GET 2 Loop PRINT 3 Sub 1 4 IFPOS Loop 5 STOP

Answer 35

None. All numbers will eventually be subtracted below zero, and even letters will be considered not positive.

Question 36

Determine the Output of the following Toy Computer code : 1 GET (8) 2 STORE length 3 GET (4) 4 GOTO Top 5 End LOAD perimeter 6 ADD length 7 STORE perimeter 8 LOAD width 9 Top SUB 1 10 STORE width 11 IFPOS End 12 LOAD perimeter 13 PRINT 14 STOP 15 length 16 width 17 perimeter 0

Answer 36

Output : 32

Question 37

How to check if this (or any other) program works correctly?

Answer 37

Testing: run the program and see if it works Enter unexpected input data * a negative or a floating-point number, e.g. 1.25 * a character, e.g. T Above all else, programmers should test “edge cases” * Does the program work with no input or only one number as input? * Does it work with very small or very large numbers? * If it works with 3 and with 1000 numbers as input, it is likely to work with 5 or 777 numbers (or anything in between) as well.