1.1 Binary Hex Number Systems

Question 1

Why do computers use binary to represent all forms of data?

Answer 1

• Any form of data needs to be converted to binary to be processed by a computer
• Data is processed using logic gates and stored in registers

Question 2

Explain the concept of overflow and why it occurs in binary addition

Answer 2

• A computer or a device has a predefined limit that it can represent or store e.g. 16-bits
• Overflow errors happen when the largest number that a CPU register can hold is exceeded.
• The number of bits that a CPU can handle is called the word size.
• When adding 2 binary numbers an overflow error occurs when a value outside this limit is stored e.g if the value is greater than 255 in an 8-bit register

Question 3

Explain the difference between the binary and denary number systems

Answer 3

• Binary base 2 system
  
  • Denary base 10 system
• Binary has 2 digits (0 and 1)
  
  • Denary has 10 digits (0-9)
• Binary place values are powers of 2
  
  • Denary place values are powers of 10

Question 4

What are the binary place values for a byte?

Answer 4

128 64 32 16 8 4 2 1

Question 5

Convert the binary number 10011011 into denary

Answer 5

155

Question 6

Convert the denary value 156 into binary

Answer 6

10011100

Question 7

What is the largest value that can be stored in 8 bits?

Answer 7

255

Question 8

What is the largest value that can be stored in 10 bits?

Answer 8

1023

Question 9

What would be the effect of shifting the bits 1 place to the left for the binary value 0001 1101

Answer 9

• Multiplying by 2
• 0001 1101 = 29
• 00111010 = 58

Question 10

What would be the effect of shifting bits 3 places to the left?

Answer 10

• multiply by 8 or multiply by 2 x 2 x 2 or multiply by 2^3
• 0000 0110 = 6
• 0011 0000 = 48

Question 11

What would be the effect of shifting bits 2 places to the right?

Answer 11

• divide by 4 or divide by 2^2
• 0001 0000 = 16
• 0000 0100 = 4

Question 12

How many bits in a byte?

Answer 12

8

Question 13

How many bits in a nibble?

Answer 13

4

Question 14

How many nibbles in 4 bytes?

Answer 14

8

Question 15

What is a register?

Answer 15

• A register is a small amount of internal memory
• Used for fast reading and writing
• It is temporary/volatile (loses data once there is no power)

Question 16

What are the rules you need to remmeber for binary addition?

Answer 16

• 0 + 1 = 1
• 1+ 1 = 2 = 0 Carry 1
• 1+1+1 = 3 = 1 Carry 1

Question 17

Add the 2 binary values 00100111 + 01001010

Answer 17

01110001

Question 18

Add the 2 binary values 01110010 + 11111001. If you tried to store the result in word size of 8 bits what error would occur?

Answer 18

Requires 9 bits (101101011) so overflow error

Question 19

What are the binary place values for a 2’s Complement byte?

Answer 19

-128 64 32 16 8 4 2 1

Question 20

What is the smallest value that can be stored in a 2’s Complement byte?

Answer 20

• -128 64 32 16 8 4 2 1
• 1 0 0 0 0 0 0 0= -128

Question 21

What is the largest value that can be stored in a 2’s Complement byte?

Answer 21

• -128 64 32 16 8 4 2 1
• 0 1 1 1 1 1 1 1 = 127

Question 22

Negative denary numbers can be represented as binary using ….

Answer 22

2’s Complement

Question 23

Convert the 2’s Complement binary number below to denary

11111111

Answer 23

-1

Question 24

Convert the 2’s Complement binary number below to denary

10001000

Answer 24

-120

Question 25

Convert the denary number below to 2's Complement binary -19

Answer 25

11101101

Question 26

Convert the denary number below to 2's Complement binary -7

Answer 26

11111001

Question 27

What is hexadecimal?

Answer 27

* Base 16 number system * 16 choices of digits (0-9, A-F) * Place values are powers of 16

Question 28

What are the place values for the hexadecimal value A7F3?

Answer 28

* 4096 256 16 1 * A 7 F 3

Question 29

What is the denary value of the hex digit A?

Answer 29

10

Question 30

What is the denary value of the hex digit E?

Answer 30

14

Question 31

What is the denary value of the hex digit 7?

Answer 31

7

Question 32

Convert the hex value AAA to Denary

Answer 32

2730

Question 33

Convert the following hex values to denary * 1F * 42 * CC

Answer 33

* 1F = 31 * 42 = 66 * CC = 204

Question 34

Convert the hex value CA to Binary

Answer 34

11001010

Question 35

Convert the following hexadecimal values to binary * B3 * 5A * B0F

Answer 35

* B3 = 1011 0011 * 5A = 0101 1010 * B0F = 1011 0000 1111

Question 36

Convert the binary value 1111 1010 to hexadecimal

Answer 36

FA

Question 37

Convert the following binary values to hexadecimal * 1011 1101 * 1010 0110 * 1111 1010 1100 1110

Answer 37

* 1011 1101 = BD * 1010 0110 = A6 * 1111 1010 1100 1110 = FACE

Question 38

Convert the hex value AB to Denary

Answer 38

171

Question 39

Convert the denary value 166 to hexadecimal

Answer 39

A6

Question 40

Convert the following denary values to hexadecimal * 22 * 42 * 170

Answer 40

* 22 = 16 * 42 = 2A * 170 = AA

Question 41

Why do we use hexadecimal?

Answer 41

* Easier for programmers to read and understand * Conversion to binary easier than denary to binary * Takes up less space when displayed or printed * Faster than binary for entering numbers

Question 42

Where is Hexadecimal used?

Answer 42

* HTML colour codes e.g. red = #FF0000 * Display MAC (Media Access Control) addresses e.g. 01-23-45-67-89-AB-CD * Display ASCII or Unicode values e.g. %41 = 65 = A * Display error codes e.g. error #404 page not found * Display memory dumps e.g. 5F 3A 09 F1

Question 43

What is ASCII?

Answer 43

* American Standard Code for Information Interchange. * It is a code for representing 128 English characters as numbers * Each character is assigned a number from 0 to 127

Question 44

How many bits does ASCII use?

Answer 44

7 bits

Question 45

How many characters can be represented using ASCII?

Answer 45

* Uses 7 bits so ... * 000 0000 to 111 1111 = 0 to 127 = 128 unique characters (2^7)

Question 46

How many bits does extended ASCII use?

Answer 46

8

Question 47

How many characters can be represented using extended ASCII?

Answer 47

* 0000 0000 to 1111 1111 = 0 to 255 = 256 unique characters (2^8)

Question 48

How many bits does Unicode use?

Answer 48

16

Question 49

How many characters can be represented using Unicode?

Answer 49

* Uses 16 bits so ... 65536 unique characters (2^16)

Question 50

Describe the difference between ASCII and Unicode

Answer 50

* ASCII uses 7 (or 8 bits) and can represent 128 (or 256 characters) * Unicode uses 16 bits and can represent 2^16 characters.

Question 51

Describe one advantage of Unicode

Answer 51

Can represent a wider range of characters and therefore more languages than ASCII

Question 52

Describe one disadvantage of Unicode

Answer 52

Each character uses more memory space than ASCII

Question 53

Describe what is meant by a character set

Answer 53

* All the characters and symbols that can be represented by a computer system. * Each character and symbol is assigned a unique value.