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# What is Floating-Point Representation in Computer Architecture?

The floating-point representation can implement operations for high range values. The numerical evaluations are carried out using floating-point values. It can create calculations easy, scientific numbers are described as follows −

The number 5,600,000 can be described as 0.56 * 107.

Therefore, 0.56 is the mantissa and 7 is the value of the exponent.

Binary numbers can also be described in exponential form. The description of binary numbers in the exponential form is called floating-point representation. The floating-point representation breaks the number into two parts, the left-hand side is a signed, fixed-point number known as a mantissa and the right-hand side of the number is known as the exponent. The floating-point values are also authorized with a sign; 0 denoting the positive value and 1 denoting the negative value.

The general structure of floating-point representation of a binary number −

x=(x_{0}*2^{0}+x_{1}*2^{1}+x_{2}*2^{2}±−−∓b_{−(n−1)}*2^{−(n−1)} )

mantissa*2^{Exponent}

In the following syntax, the decimal point is transferred left for negative exponents of two and right for positive exponents of two. Both the mantissa and the exponent are signed values enabling negative numbers and negative exponents commonly.

**Example** − Convert 111101.1000110 into floating-point value.

111101.1000110 = 1.111011000110 * 2^{5}Converted to floating-point value

→ Denotes negative sign value

In this example, the integer value is converted to a floating-point value by changing the radix point next to the signed integer and scaling up the number to the exponential form by multiplying the value with the base 2. The value remains unaltered and this phase is known as the normalized method.

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