Hi, i have problems with these three. The problem i have, is that when i need to

Question

Hi, i have problems with these three. The problem i have, is that when i need to specify the fraction part. i obtain 17bit. based on the IEEE754-2008 i take 1 bit for the sign. 5 bits for the exponent. 10 bits to mantissa. so i take the other 7 bits of my binary number after the floating point: 1 to guard bit, 1 to the round, and the other 5 to my sticky bit. after that the values i obtain are: the guard bit is 1, the round bit is 0 and the lsb of the sticky bit is 0. but what happend if these case. what rules i need to follow. Thanks.

The Bias based on IEEE 754-2008 is 15

|sing 1bit|exponent 5 bits|mantissa 10 bits|

Calculate (3.984375

Explanation / Answer

using System; using System.Text; class Float2Binary { static void Main() { Console.WriteLine("Task 09 - Binary representation of single float (IEEE754-2008 binary32) "); Console.Write(" Please enter number [{0},{1}]: ", float.MinValue, float.MaxValue); double number = 0; if (!double.TryParse(Console.ReadLine(), out number) /*|| number = float.MaxValue*/) { Console.WriteLine("Wrong FLOAT number"); return; } int sign = 0; int exponent = 0; // retrieving the single precision value if (number < 0) // first - number sign { sign = 1; number = -number; } // normalizing mantissa and extracting exponent while (number != 0.0 && (number < 1.0 || number >= 2.0)) { if (number < 1.0) // negative binary exponent { number = number * 2.0; // equals to number / 2^-1 exponent--; } else //positive binary exponent { number = number / 2.0; // equals to number / 2^-1 exponent++; } } // checking exponent for special cases if (exponent = 128) // here we have overflow (+/- INFINITY) { exponent = 128; // special case where after biasing (+127) the exponent will have all bits set to 1 (255). number = 1.0; // after extracting the leading integer part it will become 0. } Console.WriteLine(" FLOAT number Sign: " + sign); Console.WriteLine(" Exponent number: " + exponent); Console.WriteLine(" FLOAT Mantissa: " + number); if (number >= 1.0) number -= 1.0; // finally extracts the leading 1.0 from the mantissa since it is not represented in the memory Console.WriteLine(" S SEEEEEEE MMMMMMMMMMMMMMMMMMMMMMM " + " 3 32222222 22211111111110000000000 " + " 1 09876543 21098765432109876543210 " + " The result number: {0} {1} {2}", sign.ToString(), Dec2Bin(exponent+127).PadLeft(8, '0'), FractDec2Bin(number, 23).PadRight(23, '0')); Console.WriteLine(" Press Enter to exit"); Console.ReadLine(); } static string Dec2Bin(int num) { StringBuilder bin = new StringBuilder(); while (num > 0) { bin.Insert(0, num % 2); num /= 2; } return bin.ToString(); } static string FractDec2Bin(double num, int precision) { if (num == 0.0) return "0"; // otherwise enters in endless loop StringBuilder bin = new StringBuilder(); while (num > 0.0 && precision > 0) { num *= 2.0; // equals to num / 2^-1 (shifting left) int digit = 0; if (num > 1.0) // we have 1 into the last fraction position { num -= 1.0; // extracting the fration digit and goes to the next position digit = 1; } bin.Append(digit); precision--; } // perform rounding if needed if (precision == 0 && num * 2.0 > 1.0) // we have 1 as next fraction bit after precision { int pos = bin.Length-1; // starts from back (right side) while (pos >= 0 && bin[pos] == '1') // looking for the first possible zero { bin[pos] = '0'; // clears that '1' pos--; // and goes to the left } bin[pos] = '1'; // sets first possible 0 position to 1 // example 0.0011111111(1) = 0.0100000000 } return bin.ToString(); } }

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