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COMP 212 Computer Organization and Systems

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Lab 1

Objectives: The objectives of this lab is to review the number systems and explain

how computer systems define symbols through the introduction of the ASCII

character table.

Part I: Number Systems used in computers

1.0. Representation of Binary and its relations with Hexadecimal systems

All modern computer systems use the binary representation internally directly as a

result of the use of semi-conductors which can easily be switched between two levels of

voltage corresponding to 0 and 1, respectively.

In the binary system (base 2), there are only two symbols, 1 and 0, corresponding to the

two numbers. In computers, data are grouped in bytes. Each byte is 8 digits, which if

divided into two 4-bit numbers, naturally can be converted into hexadecimal numbers

easily as shown in the below table.

The binary hexadecimal conversion table.

because binary numbers are long and difficult to remember, conversion from binary to

decimal is not as easy as that to hexadecimal numbers, hexadecimal numbers are often

used as a replacement to machine code(binary).

1.1 Conversion between Decimal and Binary numbers

Binary Decimal

0000 = 0 0100 = 4 1000 = 8 1100 = C

0001 = 1 0101 = 5 1001 = 9 1101 = D

0010 = 2 0110 = 6 1010 = A 1110 = E

0011 = 3 0111 = 7 1011 = B 1111 = F

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The decimal value of the binary number 110102 is

24+ 2

3+ 2

1= 16 + 8 + 2 = 26

Decimal to Binary

Take 61 as an example.

6110 1111012

1.2 Conversion between Hexadecimal and Binary

Hexadecimal to Binary

Consider DE116,

Therefore, the binary representation ofDE116 is 1101111000012

Binary to Hexadecimal

Consider the binary string 1111101010012

The hexadecimal representation of1111101010012 is FA916

1111 1010 1001

F A 9

= FA916

1101 1110 0001

D E 1

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1.3 Conversion between Decimal and Hexadecimal

Hexadecimal to Decimal

The decimal value of the binary number A0F616is

163x10 + 16

1x15 + 16

0x6 = 40960 + 240 + 6 = 41206

Decimal to Hexadecimal

Take 561 as an example.

56110 23116

1.4 Decimal vs Binary vs Hexadecimal

Dec Hex Bin

15 0F 00001111

26 1A 00011010

79 4F 01001111

255 FF 11111111

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Byte notations

Unit Value

KB 210 Bytes = 1024 Bytes

MB 220 Bytes = 1024 KB

GB 230 Bytes = 1024 MB

TB 240 Bytes = 1024 GB

1.5 The ASCII Table: the definition of characters in computers

The ASCII table is the first computer character coding standard which assigns each

character symbol a computer code. ASCII code is intended for U.S.A. as interchange

code. Only 7 bits are used. The high bit (the 8ths bit in a bit) is used as a so called

parity bit to check for errors in communication (no need to know this part for the time

being). With the code space of 27

(128 in total) number of code values to use, it defined

all the symbols in the English language and also some logical symbols that are not

printable, but as control code. Below is the ASCII table, where the control characters

are in the code range of 00 1F, and 7F, the rest are printable characters (20 7E).

For example:

A: 4116 or 010000012 or 6510

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Exercise 1:

Please complete the rest of the table

1st

2nd

3rd

4th

Hex 0x55

Dec 110

Bin 01101001

ASCII x

Exercise 2:

Please convert the followings Hexadecimal value to ASCII code

1. 0x4D656D6F727920344742

2. 0x42696E6172792D3031

3. 0x436F6D7040504F4C5955

1.6 Application of hexadecimal

In the computer, we usually use the Hexadecimal values to represent memory

addresses.

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Exercise 3:

IfHello is stored in the memory address 0x4389, what is the memory address ofo?

Exercise 4:

If memory address is 1-byte in length, how many memory addresses it can support?

Exercise 5:

What does 1 byte shown in the above memory diagram mean? Is it the memory

address length? Please explain.

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