# Floating-point representation

A floating-point number is said to be normalized if the most significant digit of the mantissa is nonzero. For example, the decimal number 350 is normalized but 00035 is not. Regardless of where the position of the radix point is assumed to be in the mantissa, the number is normalized only if its leftmost digit is nonzero. For example, the 8-bit binary number 00011010 is not normalized because of the three leading 0' s. The number can be normalized by shifting it three positions to the left and discarding the leading O's to obtain 11010000. The three shifts multiply the number by 23 = 8. To keep the same value for the floating-point number, the exponent must be subtracted by 3. Normalized numbers provide the maximum possible precision for the floating-point number. A zero cannot be normalized because it does not have a nonzero digit. It is usually represented in floating-point by all O's in the mantissa and exponent.

Arithmetic operations with floating-point numbers are more complicated than arithmetic operations with fixed-point numbers and their execution takes longer and requires more complex hardware. However, floating-point representation is a must for scientific computations because of the scaling problems involved with fixed-point computations .. Many computers and all electronic calculators have the built-in capability of performing floating-point arithmetic operations. Computers that do not have hardware for floating-point computations have a set of subroutines to help the user program scientific problems with floating-point numbers. Arithmetic operations with floating-point numbers are discussed in Sec. 10-5.

**Frequently Asked Questions**

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