Number System

Question 1

What is the difference between ordinal and cardinal

Answer 1

represents a position of an item ( first second , third ) / number of items in a size

Question 1

What do you need to do to perform first compliment

Answer 1

Change the number to opposite

Question 1

Why are hexadecimal used

Answer 1

Because it is a more compact representation

Question 2

How do you change a number to the 2’s compliment

Answer 2

Add one to the first compliment

Question 3

How do you perform arithmetic on a signed number

Answer 3

for a signed number 1 is negative and 0 is positive

Question 4

how can logic operation be used to discover the state of the most significcant bits

Answer 4

Identify the number of signicifant bits and add 0000 to the rest

Question 5

What is a fixed point represnetation

Answer 5

The decimal is fixed

Question 6

What is a floating point representation

Answer 6

radix point is movable mantissa x 2^exponent

Question 7

Express a number in sign and magnitude vs two’s components

Question 8

for a two’c compliment number what is the formation of the number

Answer 8

the first two value must alternate

Question 9

what is the advantage of a floating number

Answer 9

greater range of numbers with a given
number of bits than fixed point.

Question 10

What is an underflow

Answer 10

Underflow occurs when very small numbers are to be
represented but there are not enough bits available.

Question 11

What is overflow

Answer 11

Overflow occurs when a number is too large to be represented with the available bits.
Overflow is particularly important when using signed binary.

Question 12

what is the formula for relative error

Answer 12

absolute error / true value x 100

Question 13

Explain how the floating point system used could be modified to allow a more accurate representation

Answer 13

Adjust the mantissa

Reallocate (one) bit; from the exponent to the mantissa

Question 14

Why are bit patterns often displayed using hexadecimal instead of binary?

Answer 14

Easier for people to understand

Question 15

Describe how an unsigned binary integer such as 010010101110 can be converted directly into hexadecimal.

The method you describe must not involve converting into decimal.

Answer 15

Put the bits into groups of four/nibbles

Convert each group of bits/nibble into a hexadecimal digit;

Question 16

What is the following in the power of 2 :
kibibyte
mebibyte
gibibyte
tebibyte

Answer 16

2 ^ 10
2^20
2^30
2^40

Question 17

What is an unsigned binary range

Answer 17

0 - 2^n - 1

Question 18

What is a signed binary range

Answer 18

-2^n -1 to (2^n-1) -1

Question 19

difference between natural numbers and real numbers

Answer 19

Natural number is used to count discrete objetct , real numbers is continous quantities

Question 20

advantages of hexadecimal

Answer 20

• compact it uses 8 binary digit
• Easier for humans to red and remember
• Easier conversion

Question 21

What is hexadecimal used for

Answer 21

used to store memory address
used to store dolor codes
used to store mac addresses
used to store error codes

Question 22

when does overflow occur

Answer 22

by adding two positive numbers or two negative numbers adding a positive and negative number cannot give an overflow

Question 23

How do you know a number is normaliseed

Answer 23

Positive mantisa starts with 0.1 and negative starts with 1.0

Question 24

Why do we normalise numbers

Answer 24

This is becus eit maximises precisionby ensuring no bits are wasted on leading zeros

Question 25

What is the difference between fixed point and floating point

Answer 25

Fixed point -Limited - Consistent range Used for finance and embedded systems Floating point - Much larger - Used for scientific computing and graphics - More precise

Question 26

Effects of a larger mantissa compared to a smaller mantissa

Answer 26

Larger mantissa means more significant figures , higher precisions Fewer mantissa means lower precision , larger rounding errors

Question 27

Effects of a larger exponent compared to a smaller exponents

Answer 27

Large rrange of values , can represent very larger numbers Smaller exponents , smaller range and more likely to have an underflow

Question 28

Why can't 0.1 be stored in binary ?

Answer 28

it produces an infinite repeating binary fraction and cannot be expressed as a finite sum of powers of 2

Question 29

Formula for absolute value

Answer 29

Stored value - True value

Question 30

Explain why the relative error is usually considered to be more important measure of error than absolute error

Answer 30

The impact of an error depends on its size relative to the number that is represented