5.4 Binary Number Systems

Question 1

Which type of binary can represent negative numbers: signed or unsigned?

Answer 1

Signed

Question 2

What is the range of decimal numbers that can be represented using unsigned binary with four bits?

Answer 2

0 to 15 (0 to 2^4 - 1)

Question 3

How many unique bit patterns can be made with 8 bits?

Answer 3

256 (2^8)

Question 4

Which of the following could be a normalized two’s complement number?
A) 1110110
B) 01101101
C) 00010101

Answer 4

B - Normalised numbers must start with 01 or 10.

Question 5

Why might fixed-point and floating-point representations of decimal numbers be inaccurate?

Answer 5

Rounding errors can occur in values that cannot be represented exactly by binary.

Question 6

Which allows for the greatest range of numbers with a given number of bits: fixed-point or floating-point?

Answer 6

Floating-point

Question 7

Why are floating-point numbers normalized?

Answer 7

To provide the maximum level of precision for a given number of bits.

Question 8

What error occurs when a number is too large to be represented with the available bits?

Answer 8

Overflow

Question 9

How is absolute error calculated ?

Answer 9

given value - actual value.

Question 10

How is Relative error calculated ?

Answer 10

relative error = actual value/
absolute error