The Binary Overflow Theorem

Key Points

• To establish a universal theorem that defines the overflow of powers of real numbers relative to their nearest smaller power of two.
• Mathematical derivation of the theorem
• Analysis of real numbers greater than one
• Examination of positive integers as exponents
• The exact relationship between a power of a real number and the nearest smaller power of two is defined
• Overflow is quantified as the difference between the power and the largest power of two not exceeding it