Topics

Binary numbers are made of powers of two; these articles discuss their properties:

• How to Find the Last Digits of a Positive Power of Two
• Patterns in the Last Digits of the Positive Powers of Two
• Cycle Length of Powers of Two Mod Powers of Ten
• Seeing Powers of Five in Powers of Two and Vice Versa
• Patterns in the Last Digits of the Positive Powers of Five
• Cycle Length of Powers of Five Mod Powers of Ten
• Ending Digits of Powers of Five Form a Binary Tree

Properties of Binary Numbers

These articles discuss properties of binary numerals:

• A Pattern in Powers of Ten and Their Binary Equivalents
• Nines in Binary

Binary Palindromes

These articles discuss binary palindromes (numbers like 1001001):

• Finding Numbers That Are Palindromic In Multiple Bases
• Counting Binary and Hexadecimal Palindromes
• The Structure of Binary/Hexadecimal Palindromes
• Counting Binary/Hexadecimal Palindromes
• In Search of Decimal/Binary/Hexadecimal Palindromes

Visualizing Binary Numbers

These articles discuss ways to visualize binary numbers:

• Visualizing Consecutive Binary Integers
• What a Binary Counter Looks and Sounds Like

Correctly Rounded Decimal to Floating-Point Conversion

These articles discuss conversion of decimal strings to floating-point binary numbers:

• Quick and Dirty Decimal to Floating-Point Conversion
• Decimal to Floating-Point Needs Arbitrary Precision
• Incorrectly Rounded Conversions in Visual C++
• Incorrectly Rounded Conversions in GCC and GLIBC
• Visual C++ and GLIBC strtod() Ignore Rounding Mode
• Correct Decimal To Floating-Point Using Big Integers
• Fast Path Decimal to Floating-Point Conversion
• strtod()’s Initial Decimal to Floating-Point Approximation
• Using Integers to Check a Floating-Point Approximation
• Bigcomp: Deciding Truncated, Near Halfway Conversions
• Properties of the Correction Loop in David Gay’s strtod()
• Incorrect Directed Conversions in David Gay’s strtod()
• Double Rounding Errors in Floating-Point Conversions
• Incorrect Decimal to Floating-Point Conversion In SQLite
• PHP Hangs On Numeric Value 2.2250738585072011e-308
• Why “Volatile” Fixes the 2.2250738585072011e-308 Bug
• A Better Fix for the PHP 2.2250738585072011e-308 Bug
• Java Hangs When Converting 2.2250738585072012e-308
• A Closer Look at the Java 2.2250738585072012e-308 Bug
• Incorrectly Rounded Subnormal Conversions in Java
• Nondeterministic Floating-Point Conversions in Java

Correctly Rounded Floating-Point to Decimal Conversion

These articles discuss conversion of floating-point binary numbers to decimal strings:

• Quick and Dirty Floating-Point to Decimal Conversion
• Incorrect Floating-Point to Decimal Conversions
• Inconsistent Rounding of Printed Floating-Point Numbers
• Fifteen Digits Don’t Round-Trip Through SQLite Reals
• 15-Digit Quick and Dirty Conversions Don’t Round-Trip

Printing the Contents of a Floating-Point Variable

These articles show different ways to display the exact contents of an IEEE 754 floating-point variable:

• Displaying the Raw Fields of a Floating-Point Number
• Hexadecimal Floating-Point Constants
• Displaying IEEE Doubles in Binary Scientific Notation
• Converting Floating-Point Numbers to Binary Strings in C