1.1 Binary and Hex

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 difference between the binary and denary number systems

Answer 2

• 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 3

What are the binary place values for a byte?

Answer 3

128 64 32 16 8 4 2 1

Question 4

Convert the binary number 10011011 into denary

Answer 4

155

Question 5

Convert the denary value 156 into binary

Answer 5

10011100

Question 6

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

Answer 6

255

Question 7

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

Answer 7

1023

Question 8

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

Answer 8

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

Question 9

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

Answer 9

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

Question 10

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

Answer 10

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

Question 11

How many bits in a byte?

Answer 11

8

Question 12

How many bits in a nibble?

Answer 12

4

Question 13

How many nibbles in 4 bytes?

Answer 13

8

Question 14

What is a register?

Answer 14

• 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 15

What is hexadecimal?

Answer 15

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

Question 16

What are the place values for the hexadecimal value A7F3?

Answer 16

• 4096 256 16 1
• A 7 F 3

Question 17

What is the denary value of the hex digit A?

Answer 17

10

Question 18

What is the denary value of the hex digit E?

Answer 18

14

Question 19

What is the denary value of the hex digit 7?

Answer 19

7

Question 20

Convert the hex value AAA to Denary

Answer 20

2730

Question 21

Convert the following hex values to denary

• 1F
• 42
• CC

Answer 21

• 1F = 31
• 42 = 66
• CC = 204

Question 22

Convert the hex value CA to Binary

Answer 22

11001010

Question 23

Convert the following hexadecimal values to binary

• B3
• 5A
• B0F

Answer 23

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

Question 24

Convert the binary value 1111 1010 to hexadecimal

Answer 24

FA

Question 25

Convert the following binary values to hexadecimal

• 1011 1101
• 1010 0110
• 1111 1010 1100 1110

Answer 25

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

Question 26

Convert the hex value AB to Denary

Answer 26

171

Question 27

Convert the denary value 166 to hexadecimal

Answer 27

A6

Question 28

Convert the following denary values to hexadecimal

• 22
• 42
• 170

Answer 28

• 22 = 16
• 42 = 2A
• 170 = AA

Question 29

Why do we use hexadecimal?

Answer 29

• 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 30

Where is Hexadecimal used?

Answer 30

• 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