Consider the number whose decimal representation M 157710 W

Consider the number whose decimal representation M = +157.7_10. What is the closest representation for M = + 157.7_10 in IEEE 754 basic single precision? Give the equivalent hexadecimal pattern bar eta, the number bar M that bar eta exactly represents and the error Delta eta. In a C program, declare a float, and set its value to + 157.7. Then, print out the value of the variable in hexadecimal. Docs it match your answer in part (A)?

Solution

There are a few approaches to speak to genuine numbers on PCs. Settled point puts a radix point some place amidst the digits, and is proportional to utilizing whole numbers that speak to bits of some unit. For instance, one may speak to 1/100ths of a unit; in the event that you have four decimal digits, you could speak to 10.82, or 00.01. Another approach is to utilize rationals, and speak to each number as the proportion of two whole numbers.

Skimming point representation – the most well-known arrangement – utilizes experimental documentation to encode numbers, with a base number and a type. For instance, 123.456 could be spoken to as 1.23456 × 102. In hexadecimal, the number 123.abc may be spoken to as 1.23abc × 162. In paired, the number 10100.110 could be spoken to as 1.0100110 × 24.

Coasting point takes care of various representation issues. Altered point has a settled window of representation, which limits it from speaking to substantial or little numbers. Additionally, settled indicate is inclined lost accuracy when two vast numbers are separated.

Gliding point, then again, utilizes a kind of \"sliding window\" of exactness fitting to the size of the number. This permits it to speak to numbers from 1,000,000,000,000 to 0.0000000000000001 easily, keeping in mind augmenting accuracy (the quantity of digits) at both closures of the scale.