"EXPONENT CALCULATION OF FLOATING-POINT NUMBERS WITH SHIFTED ENCODING A POZITIVE ZERO"
O. V. SAMOSHCHENKO · Scientific papers of Donetsk National Technical University Series Informatics Cybernetics and Computer Science · 2025
"The rule for calculating the exponent of floating-point numbers in the shifted encoding system with positive zero is indicated, which provides for the original representation of exponents in a combination of a complementary code and a code with positive zero. Mathematical expressions are formulated to fix the overflow of the exponent of the normalized and denormalized mantissa product, according to which an arithmetic device is synthesized. It is shown that in the absence of overflow, the correct code of the exponent of the mantissa product with a violation of normalization is formed by adding a polynomial of a unit constant. The correctness of the sum of exponents at the output of the adder is determined by the output carry and the sign bit of the exponent of the product. Overflow of the bit grid of the mantissa product with a violation of normalization is determined by the combination of the signs of overflow of the normalized code and the zero value of the code at the main outputs of the exponent adder. The range of change of the total sum at the adder outputs when calculating exponents in the system of shifted codes with positive zero is analytically determined. Logical expressions are synthesized for fixing the polarity of overflow in the arithmetic device. The correctness of using the code of converted operands when calculating binary values of exponents is confirmed in examples."