Chapter 2 - Data Representation In Computer Systems

Question 1

True or False

The organization of any computer depends considerably on how it represents numbers, characters, and control information

Answer 1

True

The organization of any computer depends considerably on how it represents numbers, characters, and control information

Question 2

What is a bit?

Answer 2

• A contraction of binary digit
• The most basic unit of information in a digital computer
• Has a value of either 0 or 1

Question 3

What does the following definition describe:

• A contraction of binary digit
• The most basic unit of information in a digital computer
• Has a value of either 0 or 1

Answer 3

A bit

Question 4

What is the contraction of the word “binary digit”?

Answer 4

Bit

Question 5

What is the contraction of the word “bit”?

Answer 5

Binary digit

Question 6

True or False:

A bit is the most basic unit of information in a digital computer

Answer 6

True

A bit is the most basic unit of information in a digital computer

Question 7

True or False:

A bit can be any number, ranging from 0 to positive infinity

Answer 7

False

A bit can either be 0 or 1

Question 8

What values can a bit contain?

Answer 8

Either 0 or 1

Question 9

What are some ways a bit can be represented in the real world?

Answer 9

• On/Off
• High/Low

Question 10

What is a byte?

Answer 10

A collection of 8 bits

Question 11

What does the following definition describe:

A collection of 8 bits

Answer 11

A byte

Question 12

True or False

18 bits make up a byte

Answer 12

False

8 bits make up a byte

Question 13

What is a computer word?

Answer 13

Two or more adjacent bytes that are sometimes addressed and always manipulated collectively

Question 14

What does the following definition describe:

Two or more adjacent bytes that are sometimes addressed and always manipulated collectively

Answer 14

A computer word

Question 15

What is word size?

Answer 15

The representation of the size of data that is handled most efficiently by a particular architecture

Question 16

What does the following definition describe:

The representation of the size of data that is handled most efficiently by a particular architecture

Answer 16

Word Size

Question 17

What are some examples of word sizes?

Answer 17

• 16 bits
• 32 bits
• 64 bits

Question 18

What is a nibble/ nybble?

Answer 18

One of two 4-bit halves of a byte. Bytes consist of one high-order and one low-order nibble.

Question 19

What does the following definition describe:

One of two 4-bit halves of a byte. Bytes consist of one high-order and one low-order nibble.

Answer 19

A nibble or nybble

Question 20

True or False:

Because each bit of a byte has a value within a positional numbering system, the nibble containing the most-valued binary digit is called the low-order nibble, and the other half the high-order nibble

Answer 20

False

Because each bit of a byte has a value within a positional numbering system, the nibble containing the least-valued binary digit is called the low-order nibble, and the other half the high-order nibble

Question 21

What is a weighted numbering system?

Answer 21

A numeration system in which a value is represented through increasing powers of a radix (or base)

Question 22

What does the following definition describe:

A numeration system in which a value is represented through increasing powers of a radix (or base)

Answer 22

A weighted numbering system

Question 23

What is an example of a weighted numbering system?

Answer 23

• Binary
• Decimal

Question 24

What is a radix?

Answer 24

The base of a number system

Question 25

What does the following definition describe:

The base of a number system

Answer 25

Radix

Question 26

True or False:

The set of valid numerals for a positional numbering system is equal in size to the radix of that system

Answer 26

True

The set of valid numerals for a positional numbering system is equal in size to the radix of that system

Question 27

What would be the largest valid number in the decimal system?

Answer 27

9

The radix of the decimal system is 10, and the set of valid numerals are all numbers between 0 and 9

Question 28

What are the two most important radices in computer science?

Answer 28

• Binary (base 2)
• Hexadecimal (base 16)

Question 29

What values are allowed in hexadecimal?

Answer 29

0-9, A, B, C, D, E, F

Question 30

What is the representation of the following:

243.51₁₀

Answer 30

243.51₁₀ = (2 x 10²) + (4 x 10¹) + (3 x 10⁰) + (5 x 10^-1) + (1 x 10^-2)

Question 31

What is the following representation:

(1 x 2⁴) + (0 x 2³) + (1 x 2²) + (1 x 2¹) + (0 x 2⁰)

Answer 31

10110₂ = (1 x 2⁴) + (0 x 2³) + (1 x 2²) + (1 x 2¹) + (0 x 2⁰)

Question 32

Convert 538₁₀ into Base 8 using subtraction

Answer 32

Answer:

538₁₀ = 1032₈

Question 33

Convert 538₁₀ into base 8 using division

Answer 33

Answer:

538₁₀ = 1032₈

Question 34

Convert 147₁₀ into binary

Answer 34

Answer

147₁₀ = 10010011₂

Question 35

True or False:

A binary number with N bits can represent unsigned integers from 0 to 2^N + 1

Answer 35

False

A binary number with N bits can represent unsigned integers from 0 to 2^N − 1

Ex: 4 bits => 2⁴-1 = 16-1 = 15

Question 36

How many unsigned integers can 32 bits represent?

Answer 36

32 bits => 2³²-1 = (4.294967296 x 10⁹)- 1

Question 37

What is overflow?

Answer 37

• A condition where a register is not large enough to contain the result of an arithmetic operation
• In signed arithmetic operations, overflow is detectable when the carry into the sign bit does not equal the carry out from the sign bit

Question 38

What does the following definition describe:

• A condition where a register is not large enough to contain the result of an arithmetic operation
• In signed arithmetic operations, overflow is detectable when the carry into the sign bit does not equal the carry out from the sign bit

Answer 38

Overflow