Bits, Bytes And Number Bases

Question 1

Define Sig Fig (Significant figures) in terms of binary numbers

Answer 1

All digits except leading / trailing 0’s where they are placeholders.

Question 2

Define a floating point number in terms of binary numbers

Answer 2

a real number represented by a sign, some significant digits and a power of two.

Question 3

Define precision in terms of binary numbers

Answer 3

The maximum number of significant digits that can be represented in the mantissa. Precise = More bits in mantissa. Range = more bits in exponent.

Question 4

Define normalisation in terms of binary numbers

Answer 4

Only one digit before the decimal place with an exponent for magnitude. This ensures a unique representation of a number and maximises precision for a given number of bits.

Question 5

Define absolute error in terms of binary numbers

Answer 5

The magnitude of difference between the actual and rounded number

Question 6

Define relative error in terms of binary numbers

Answer 6

The absolute error / the actual number

Question 7

Define underflow in terms of binary numbers

Answer 7

A value is too small to be stored in a given number of bits

Question 8

Define overflow in terms of binary numbers

Answer 8

A value is too large to be stored in a given number of bits

Question 9

Define a hexadecimal number

Answer 9

A number using 16 possible characters instead of just the 10 (0-9) we use for base 10 (decimal number system)

Question 10

Define a binary number

Answer 10

A number using 2 possible character instead of the 10 we use for the decimal number system.

Question 11

Explain how to convert a binary number to a decimal number.

Answer 11

Create a table with each character of the binary number as a column. Multiply each row from right to left by 2^n where n starts at 0 and add all the answers together

Question 12

Explain how to convert a decimal number to a hexadecimal number.

Answer 12

Create a table with each character of the decimal number as a column. Multiply each row from right to left by 16^n where n starts at 0 and add all the answer together

Question 13

Explain how to convert a binary number to a hexadecimal number

Answer 13

split the binary number into 4 character numbers (nibbles) and convert each nibble into a hexadecimal digit as each 4 character binary number has a maximum value of 15 or F in hexadecimal. Then just join the digits together and create the hexadecimal number.

Question 14

Explain how binary multiplication works

Answer 14

Split one of the two numbers into the parts that involve 1. For example, if you are multiplying 10101 by 10001, it would be the same as multiplying 10101 * 10000 + 10101 * 1.

Question 15

Explain how a negative binary number works

Answer 15

They create a complement of a positive number by using the most significant digit as the negative form of itself.

Question 16

Define a natural number

Answer 16

Any positive integer (Represented with an N

Question 17

Define an integer

Answer 17

Any whole number. Includes negative numbers (Represented with a Z)

Question 18

Define a rational number

Answer 18

Any number that can be written as a fraction. That includes integers at they can be written with an /1 (Represented with a Q)

Question 19

Define an irrational number

Answer 19

Any number that cannot be written as a fraction. Examples include π and √2. (Represented as Q’ as they complement Q or rational numbers)

Question 20

Define a real number

Answer 20

Encompasses both rational and irrational numbers. Does not include every number as some are considered imaginary such as i (√-1) or infinity (∞) (Represented by an R)

Question 21

Define an ordinal number

Answer 21

A number that describes an objects location in a list. For example 3rd is an ordinal number as it describes a location in a list of objects.

Question 22

Explain the difference between the kilo series of bytes and the kibi series of bytes

Answer 22

A kilobyte is 10^3 whilst a kibibyte is 2^10. Each bi byte is 2^10n whilst each ga byte is 10^3n. So:
Kilo = 10^3
Mega = 10^6
Giga = 10^9
Tera = 10^12
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Kibi = 2^10
Mebi = 2^20
Gibi = 2^30
Tebi = 2^40