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**ANSWER-1:-**

**1(a)(i):**

In computing, a fixed-point number representation is a real data type for a number that has a fixed number of digits after (and sometimes also before) the radix point (after the decimal point ‘.’ in English decimal notation). Fixed-point number representation can be compared to the more complicated (and more computationally demanding) floating-point number representation.

Fixed-point numbers are useful for representing fractional values, usually in base 2 or base 10, when the executing processor has no floating point unit (FPU) or if fixed-point provides improved performance or accuracy for the application at hand. Most low-cost embedded microprocessors and microcontrollers do not have an FPU.

**1(a)(ii):**

Roundoff error occurs because of the computing device’s inability to deal with certain numbers. Such numbers need to be rounded off to some near approximation which is dependent on the word size used to represent numbers of the device.

**1(a)(iii):**

Floating-point number representations allow for the existence of two zeros, often denoted by −0 (negative zero) and +0 (positive zero), regarded as equal by the numerical comparison operations but with possible different behaviors in particular operations.

**1(c):**

Appox true value is :

3.1415926535897932384626433832795

this is called the level of accuracy or to how many significant digits places

pi appox equal 22/7 or 355/113

Depending on the Level of Accuracy desired

here some other value appox value for it

31 ^ (1/3)

54648/17395 accurate to 7 decimal places

(2143/22)^.25 or (97 9/22)^ (1/4) accurate to 9 decimal places

833009/ 265155 = pi to 10 decimal places

52163/16604 pi is accurate to the true value to six or seven decimal places

144029661/45846065

69305155/22060516

5419351/1725033

52,163/16,604 = 3.1415923873765357745121657431944

312689/99532

312689/99532

3 + 4/28 – 1/(790 + 5/6) appox PI