Question

Using the IEEE 754 floating-point format, write down the bit pattern that would represent$-1/4$. Can you represent$-1/4$exactly?

Short answer

The IEEE 754 floating-point format of$-1/4$ is 1.011111010000000000 with the exponent -2.

Step-by-step solution

Determine the IEEE 754 floating-point format.

The floating point will have the scientific notation with a single digit to the left of the decimal point. The normalized scientific notation will have no leading 0s. The next part will be the fraction part, which is called the mantissa. The exponent field will have the value of the floating-point arithmetic.

Determine the IEEE 754 floating-point format.

The given number is $-1/4$:

Rewriting the number in a decimal form, we have

$-\frac{1}{4}=-0.25$

Now, convert the given number to a binary number with scientific notation:.

$-0.25=10111110100000000000000000000000$

1 represents the sign of the number and the exponent is –2.

Value	sign	Exponent
1 0111110100000000000000000000000	-	-2

The value is the exact value of $-1/4$in the IEEE 754 floating-point format.