Question

Question: What do you get if you add$-\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$to itself 4 times? What is$-\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.\times 4$ ? Are they the same? What should they be?

Short answer

The value of adding –1/4 four times and the value of multiplying -–1/4 by 4 are the same.

Step-by-step solution

Determine the IEEE 754 floating-point format.

The number will be converted into a binary number. The sign will be represented as a separate bit. The floating-point will have the scientific notation with a single digit to the left of the decimal point. The scientific notation will be normalized—it will have no leading 0s. The exponent field will have the value of the floating-point arithmetic.

Determine that the given statement is true.

The given number –1/4.

The decimal value of the given number is $-0.25$

Add $-0.25$four times with itself..

Multiplyingby 4, we have

Thus, it is clear that the value of adding –1/4 four times and the value of multiplying –1/4 by 4 are the same.