Mantissa- why is the first digit not included?

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I'll put the link to the page and the issue I'm querying right here as the system won't let me put the link in the first field. Link : https://codegym.cc/quests/lectures/en.questsyntaxpro.level04.lecture07 (Number 3). My question is not re: a task but the theory part of this lesson (specifically number 3 on this page) which talks about the mantissa and how only 15 digits max can be allocated to a real number in the double variable (I'm paraphrasing). As far as I know and I could be wrong, but the mantissa also includes the first digit in

10000000.00000000

, which is 1. In this lesson, why is the 1 not included in the matissa or the 15 digits limit of a double variable memory allocation?

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Thomas

Level 41 , Bayreuth, Germany

19 November 2024, 14:10

Java handles float and double (compare JLS) as specified in the IEEE 754. Here you can read (for double), that 1 bit is used for the sign, 11 for the exponent and 52 for the fraction. If you calculate the maximum number 52 bits can hold, then you will see its all 15 digit (decimal) numbers and a good bunch of 16 digit numbers. The exact number you can calculate yourself (maybe with the help of a little Java program ;) )

// 4503599627370495
System.out.println(new BigInteger("1111 11111111 11111111 11111111 11111111 11111111 11111111".replaceAll("\\h",""), 2).toString(10));

As a little exercise you could look up what the fraction part of float (single precision) is and calculate its maximum decimal value.

Christy QA Automation Engineer

20 November 2024, 17:37

Thanks for your response. I'll delve into it further to understand better.