# Floating-Point Representation

The floating-point representation of a number has two parts. The first part represents a signed, fixed-point number called the mantissa. The second part designates the position of the decimal (or binary) point and is called the exponent. The fixed-point mantissa may be a fraction or an integer. For exam ple, the decimal number +6132.789 is represented in floating-point with a fraction and an exponent as follows:

Fraction

+0.6132789

Exponent +04

The value of the exponent indicates that the actual position of the decimal point is four positions to the right of the indicated decimal point in the fraction. This representation is equivalent to the scientific notation +0.6132789 X 10+4. Floating-point is always interpreted to represent a number in the follow ing form:

mxr'

Only the mantissa m and the exponent e are physically represented in the register (including their signs). The radix r and the radix-point position of the mantissa are always assumed. The circuits that manipulate the floating-point numbers in registers conform with these two assumptions in order to provide the correct computational results. A floating-point binary number is represented in a similar manner except that it uses base 2 for the exponent. For example, the binary number + 1001.11 is represented with an 8-bit fraction and 6-bit exponent as follows:

The fraction has a 0 in the leftmost position to denote positive. The binary point ofthe fraction follows the sign bit but is not shown in the register. The exponent has the equivalent binary number +4. The floating-point number is equivalent to

m x 2' = +(.1001110), x z+•

**Frequently Asked Questions**

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