02 Section 7 - Binary and Hexadecimal

Question 1

What base is denary/decimal in?

Answer 1

base-10

Question 2

What base is binary in?

Answer 2

base-2

Question 3

What are the units for 8 bits?

Answer 3

128 64 32 16 8 4 2 1

each column is just a power of 2

Question 4

How do you convert from binary to decimal and back again?

Answer 4

Always lay out columns with the amount which can be in them, and work logically to work it out both ways

Question 5

How do you add binary numbers?

Answer 5

By using column addition

• work from right to left
• 0+0 = 0, 0+1 = 1, 1+1 = 10

Question 6

What is an overflow errors?

Answer 6

Overflow errors occur when a number has too many bits

• an overflow error from the computer getting extra bits, instead the computer will see the extra digit as an overflow error
• overflow flags are used to show that an overflow error has occurred

Question 7

What are the problems with a computer and overflow errors?

Answer 7

An overflow error can lead to a loss of data and a loss of accuracy in the answer.
It could also cause software to crash if the program doesn’t have a way of dealing with the extra bit

Question 8

What is Binary Shift/Logical Shift?

Answer 8

Binary shift is when you move every bit in a binary number left or right a certain number of places

• left shifts times the number by powers of 2
• right shifts divide the numbers by powers of 2

Question 9

What problems can left and right shifts cause?

Answer 9

Left shifts can cause overflows
Right shifts can ‘drop off’
-these can both cause a loss of accuracy/data

Question 10

What base are hexadecimal numbers in?

Answer 10

base-16

Question 11

What does a single hex character represent in denary numbers or binary numbers?

Answer 11

One hex digit can represent

• decimal- 0-15
• binary- 4 bits (a nibble)

Question 12

Why do programmers prefer hex when coding?

Answer 12

• it is simpler to remember large numbers in hex
• due to hex numbers being shorter, there is less chance of input errors
• easier to convert between binary and hex than binary and denary

Question 13

How do base-16 represent all the characters?

Answer 13

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

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

Question 14

What are the units in hex?

Answer 14

4096 256 16 1

Question 15

How do you convert from Binary to Hex?

Answer 15

Convert Binary to Hex by splitting it into nibbles

• draw a table and convert each nibble into hex
• then put the hex digits together

Question 16

How do you convert from Hex to Binary?

Answer 16

For Hex to Binary, use each character’s denary value

• convert each hex digit into binary
• then put the binary nibbles together