CHAPTER 4: Arithmetic for Computers

Question 1

arithmetic logic unit (ALU)

Answer 1

hardware that performs addition, subtraction, and usually logical operations such as AND and OR

Question 2

overflow

Answer 2

Question 3

normalized

Answer 3

number in floating-point notation that has no leading 0s

Question 4

floating point

Answer 4

computer arithmetic that represents numbers in which the binary point is not fixed

Question 5

overflow (floating-point)

Answer 5

situation in which a positive exponent becomes too large to fit in the exponent field

Question 6

underflow (floating-point)

Answer 6

situation in which a negative exponent becomes too large to fit in the exponent field

Question 7

double precision

Answer 7

floating-point value represented in a 64-bit doubleword

Question 8

single precision

Answer 8

floating-point value represented in a 32-bit word

Question 9

exception (interrupt)

Answer 9

unscheduled event that disrupts program execution; used to detect overflow

Question 10

interrupt

Answer 10

exception that comes from outside of the processer

Question 11

guard

Answer 11

first of two extra bits kept on the right during intermediate calculations of floating-point numbers; used to improve rounding accuracy

Question 12

round

Answer 12

Method to make the intermediate floating-point result fit the floating-point format; the goal is typically to find the nearest number that can be represented in the format. It is also the name of the second of two extra bits kept on the right during intermediate floating-point calculations, which improves rounding accuracy

Question 13

units in the last place (ulp)

Answer 13

number of bits in error in the least significant bits of the significand between the actual number and the number that can be represented

Question 14

sticky bit

Answer 14

bit used in rounding in addition to guard and round that is set whenever there are nonzero bits to the right of the round bit

Question 15

fused multiply add

Answer 15

floating-point instruction that performs both a multiply and an add, but rounds only once after the add

Question 16

fallacy: just as a left shift instruction can replace an integer multiply by a power of 2, a right shift is the same as an integer division by a power of 2

Question 17

pitfall: floating-point addition is not associative

Question 18

fallacy: parallel execution strategies that work for integer data types also work for floating-point data types