CHAPTER 5: Representing Numerical Data

Question 1

How do computers store all data and program instructions?

a) As decimal numbers.
b) As ASCII characters
c) As binary numbers.
d) As algebraic equations.

Answer 1

c) As binary numbers.

Question 2

The binary numbers in a computer might represent

a) images.
b) numbers.
c) characters.
d) All of the above

Answer 2

d) All of the above

Question 3

What numbers are generally manipulated as characters?

a) Zip code.
b) Telephone number.
c) Grade point average.
d) Both a and c.

Answer 3

d) Both a and c.

Question 4

When the number to be expressed is outside of the integer range of the computer (too large or too small), or when the number contains a fractional part it must be stored as a(n)

a) constant.
b) exponent.
c) complement.
d) real number.

Answer 4

d) real number.

Question 5

An 8-bit storage location can store any unsigned integer of value between 0 and

a) 7
b) 16
c) 255
d) 512

Answer 5

c) 255

Question 6

What does BCD stand for?

a) Binary-Coded Decimal
b) Binary Calculating Device
c) Binary Common Denominator
d) Binary Character Data

Answer 6

a) Binary-Coded Decimal

Question 7

What is the range of a 1 byte number stored in BCD format?

a) 0-9
b) 0-99
c) 0-999
d) 0-9999

Answer 7

b) 0-99

Question 8

How many BCD digits can be stored in one byte?

a) 1
b) 2
c) 7
d) 255

Answer 8

b) 2

Question 9

What is the most common way to represent negative integers in binary form?

a) As BCD
b) Using 2’s complement
c) Using sign-and-magnitude
d) None of the above

Answer 9

b) Using 2’s complement

Question 10

If we complement the value twice, it will

a) be twice as big.
b) return to its original value.
c) cause an overflow error.
d) reset the carry flag.

Answer 10

b) return to its original value.

Question 11

A combination of numbers that produces a result outside the available range is known as

a) overload.
b) overflow.
c) spillover.
d) wraparound.

Answer 11

b) overflow.

Question 12

Changing every 0 to a 1 and every 1 to a 0 is also known as

a) reversion.
b) inversion.
c) diversion.
d) conversion.

Answer 12

b) inversion.

Question 13

Using sign-and-magnitude representation, the largest positive number that can be stored in 8 bits is

a) 7
b) 127
c) 255
d) 512

Answer 13

b) 127

Question 14

Using sign-and-magnitude representation, if the leftmost bit is 1 the number is

a) positive.
b) negative.
c) an error.
d) a character

Answer 14

b) negative.

Question 15

If both inputs to an addition have the same sign, and the output sign is different then

a) the leftmost bit should wrap around.
b) the leftmost bit should be disregarded.
c) the range is insufficient to hold the result.
d) you must take the complement of the result.

Answer 15

c) the range is insufficient to hold the result.

Question 16

Using sign-and-magnitude representation, storing the number -12 in 4 bits is

a) 1100
b) 0011
c) 0100
d) impossible.

Answer 16

d) impossible.

Question 17

In 1’s and 2’s complement representations, a negative number begins with

a) -1
b) 0
c) 1
d) -0

Answer 17

c) 1

Question 18

How do you find the 2’s complement of positive numbers?

a) Invert the numbers
b) Invert the numbers and add one
c) Invert the numbers and wrap around the leftmost bit
d) Do nothing, the complement is the same as the original

Answer 18

b) Invert the numbers and add one

Question 19

How do you find the 2’s complement of negative numbers?

a) Invert the numbers.
b) Invert the numbers and add one.
c) Invert the numbers and wrap around the leftmost bit.
d) Do nothing, the complement is the same as the original.

Answer 19

b) Invert the numbers and add one.

Question 20

When adding two numbers using 2’s complement, carries beyond the leftmost digit are

a) inverted.
b) ignored.
c) shifted left.
d) shifted right.

Answer 20

b) ignored.

Question 21

What is the 8-bit 2’s complement representation for -35?

a) 11011101
b) 01011101
c) 11011100
d) 11011111

Answer 21

a) 11011101

Question 22

To correct for carries and borrows that occur when large numbers must be separated into parts to perform additions and subtractions, we use

a) a bit hold.
b) a carry flag.
c) an error flag.
d) an overflow flag.

Answer 22

b) a carry flag.

Question 23

What is the number 12.345 x 10² without using exponential notation?

a) 0.12345
b) 123.45
c) 1234.5
d) 12345

Answer 23

c) 1234.5

Question 24

In excess-50 notation, an exponent can range from

a) 0 to 50
b) -50 to 49
c) -49 to 50
d) -99 to 99

Answer 24

b) -50 to 49

Question 25

In excess-50 notation, an exponent equaling 17 is stored as

a) -37
b) 17
c) 67
d) 87

Answer 25

c) 67

Question 26

Shifting numbers left and increasing the exponent until leading zeros are eliminated is called

a) conversion.
b) factorization.
c) normalization.
d) excess notation.

Answer 26

c) normalization.

Question 27

The leftmost bit in an IEEE standard floating point number represents

a) the exponent.
b) the mantissa.
c) the sign of the mantissa.
d) the sign of the exponent.

Answer 27

c) the sign of the mantissa.

Question 28

The exponent of a floating point number is stored using

a) excess N notation.
b) one’s complement.
c) two’s complement.
d) binary coded decimal.

Answer 28

a) excess N notation.

Question 29

In the IEEE 754 standard 32 bit single-precision floating point format, how many bits are allocated to the exponent?

a) 1
b) 2
c) 7
d) 8

Answer 29

d) 8

Question 30

In the IEEE 754 standard 32 bit single-precision floating point format, how many bits are allocated to the mantissa?

a) 8
b) 16
c) 23
d) 24

Answer 30

c) 23

Question 31

With floating point numbers, to add and subtract require that

a) the sign in each number be equal.
b) the mantissa in each number be equal.
c) the exponents in each number be equal.
d) you convert to decimal to perform the operation.

Answer 31

c) the exponents in each number be equal.

Question 32

In the normalized IEEE 754 standard 32 bit single-precision floating point format, the leading bit of the mantissa is

a) the sign bit.
b) not stored.
c) always a zero.
d) used for larger exponents.

Answer 32

b) not stored.

Question 33

In the IEEE 754 standard 32 bit single-precision floating point format the number “zero” is

a) impossible to represent.
b) treated as a special case.
c) has a mantissa of all ones.
d) has an exponent of all ones.

Answer 33

b) treated as a special case.

Question 34

The Department of Motor Vehicles is developing a software program that uses a variable to count the number of cars being sold each day. The maximum number of cars sold is expected to be several million over the life of the program and there are no fractional sales. What data type will you use for this variable?

a) float 32-bit
b) float 64-bit
c) integer long 64-bit
d) integer short 32-bit

Answer 34

c) integer long 64-bit

Question 35

Calculations with floating point numbers

a) are faster than integer calculations.
b) are more precise than integer calculations.
c) typically require less storage space than integers for the results. d) None of the above.

Answer 35

d) None of the above.