Integer representation and arithmetic pt1

Question 1

What is a bit

Answer 1

A bit is a single binary digit, i.e., 0 or 1

Question 2

What is a byte

Answer 2

A byte is an 8-element sequence of bits

Question 3

What is a word

Answer 3

A word is a w-element sequence of bits

Question 4

How does binary relate mathematically to integers

Answer 4

Mapping representation

Question 5

What is little-endian ordering for bit sequences?

Answer 5

Least sig value stored first

Question 6

What is big-endian ordering?

Answer 6

Question 7

Which bit-sequence ordering is used most often? And why?

Answer 7

Little-endian (right-to-left)
Because it makes it such that the least sig bit is at the start (great for operating on it)

Question 8

How do single binary operators apply to a string of bits

Answer 8

Applies to each element (eg not)

Question 9

How do multi-binary operators (eg: AND OR XOR etc.) apply to two strings of bits

Answer 9

Applies to each element combined (make sure to pad with zeros on sig side)

Question 10

What is the Hamming weight of a string of bits

Answer 10

Question 11

What is the Hamming distance of two strings of bits

Answer 11

Question 12

How does base expansion of a string of digits work

Answer 12

Multiply by base to the power of index (in little endian). Eg 2^0 2^1 etc.

Question 13

How to convert between hexadecimal string and a binary string

Answer 13

Each hex character represents 4 bits so can expand

Question 14

How does a binary left (or right) shift work

Answer 14

For left shift multiply by 2^y (or inverse for right shift)

Question 15

How does the sign magnitude approach work

Answer 15

• 1st bit is reserved for the sign
• Means that there is pos and neg zero
• Smaller range than twos-compliment

Question 16

How does the sign magnitude number line look

Answer 16

Question 17

How does the twos compliment approach work

Answer 17

• 1 at the start still signifies negative
• 10000000 is the most sig negative value
• Any additional 1 counts upwards
• 1 more possible value since no pos neg zero

Question 18

What does the twos compliment number line look like

Answer 18

Question 19

How many states possible in an n bit word

Answer 19

2^n or max binary val of 2^n -1