CS 330 Chapter 10

The most important floating-point representation is defined in IEEE Standard _________, adopted in 1985 and revised in 2008.

754

________ is when the result may be larger than can be held in the word size being used. A. Overflow B. Arithmetic shift C. Underflow D. Partial product

A. Overflow

_________ are included in IEEE 754 to handle cases of exponent underflow. A. Subnormal numbers B. Guard bits C. Normal numbers D. Radix points

A. Subnormal numbers

Positive numbers less than 2^-127 are called ________. A. positive underflow B. positive overflow C. negative underflow D. negative overflow

A. positive underflow

Moving the sign bit to the new leftmost position and filling in with copies of the sign bit is called _________. A. sign extension B. range extension C. bit extension D. partial extension

A. sign extension

The _________ is that part of the computer that actually performs arithmetic and logical operations on data.

Arithmetic and Logic Unit (ALU)

__________ means that the number is too small to be represented and it may be reported as 0. A. Negative underflow B. Exponent underflow C. Positive underflow D. Significand underflow

B. Exponent underflow

__________ representation is almost universally used as the processor representation for integers. A. Biased B. Twos compliment C. Sign-magnitude D. Decimal

B. Twos compliment

Although considered obsolete, the term _________ is sometimes used instead of significand. A. minuend B. mantissa C. base D. subtrahend

B. mantissa

Negative numbers greater than 2^-127 are called _________. A. negative overflow B. negative underflow C. positive overflow D. positive underflow

B. negative underflow

Positive numbers greater than (2 - 2^-23) x 2^-128 are called _________. A. negative underflow B. positive overflow C. positive underflow D. negative overflow

B. positive overflow

__________ is when a positive exponent exceeds the maximum possible exponent value. A. Significand underflow B. Significand overflow C. Exponent overflow D. Exponent underflow

C. Exponent overflow

_________ formats extend a supported basic format by providing additional bits in the exponent and in the significand. A. Arithmetic B. Basic C. Extended precision D. Interchange

C. Extended precision

__________ involves the generation of partial products, one for each digit in the multiplier, which are then summed to produce the final product. A. Addition B. Subtraction C. Multiplication D. Division

C. Multiplication

The most common scheme in implementing the integer portion of the ALU is: A. sign-magnitude representation B. biased representation C. twos complement representation D. ones complement representation

C. twos complement representation

Negative numbers less than -(2 - 2^-23) x 2^128 are called _________. A. positive underflow B. positive overflow C. negative underflow D. negative overflow

D. negative overflow

In ________ representation the rule for forming the negation of an integer is to invert the sign bit. A. ones complement B. twos complement C. biased D. sign-magnitude

D. sign-magnitude

Booth's algorithm performs more additions and subtractions than a straightforward algorithm.

F

For base 2 representation, a normal number is one in which the most significant bit of the significand is zero.

F

It is not necessary for the ALU to signal when overflow occurs.

F

Overflow can only occur if there is a carry.

F

Overflow is a less serious problem because the result can generally be satisfactorily approximated by 0.

F

Actual floating-point representations include a special bit pattern to designate zero.

T

Addition and subtraction can be performed on numbers in twos complement notation by treating them as unsigned integers.

T

An advantage of biased representation is that non-negative floating-point numbers can be treated as integers for comparison purposes.

T

Both sign-magnitude representation and twos complement representation use the most significant bit as a sign bit.

T

Compared with addition and subtraction, multiplication is a complex operation, whether performed in hardware of software.

T

For each 1 on the multiplier, an add and a shift operation are required; but for each 0 only a shift is required.

T

One drawback of sign-magnitude representation is that there are two representations of 0.

T

One of the trade-offs of floating-point math is that many calculations produce results that are not exact and have to be rounded to the nearest value that the notation can represent.

T

The numbers represented in floating-point notation are not spaced evenly along the number line, as are fixed-point numbers.

T

With a fixed-point notation it is possible to represent a range of positive and negative integers centered on or near 0.

T

_________ format covers five floating-point representations, three binary and two decimal, whose encodings are specified by the standard, and which can be used for arithmetic.

basic

IEEE 754-2008 defines an __________ format as a format with a precision and range that are defined under user control.

extendable precision

_________ representation is when the radix point is fixed and assumed to be to the right of the rightmost digit.

fixed point

The use of subnormal numbers is referred to as _________ underflow.

gradual

The register contains additional bits, called __________, which are used to pad out the right end of the significand with 0s.

guard bits

__________ format is a fully specified, fixed-length binary encoding that allows data interchange between different platforms and that can be used for storage.

interchange

A __________ is one in which the most significant digit of the significand is nonzero.

normal number

If two numbers are added, and they are both positive or both negative, then _________ occurs if and only if the result has the opposite sign.

overflow

_________ occurs when an arithmetic operation results in an absolute value greater than can be expressed with an exponent of 128.

overflow

When the divisor is able to divide the number, a 1 is placed in the quotient and the divisor is subtracted from the partial dividend; the result is referred to as a ________.

partial remainder

Extending the range of numbers that can be expressed by increasing the bit length is referred to as __________.

range extension

__________ is when the result is put back into the floating-point format and the extra bits must be eliminated in such a way as to produce a result that is close to the exact result.

rounding

"To subtract one number from another, take the twos complement of the subtrahend and add it to the minuend" is the _________ rule.

subtraction