Convert Decimal to IEEE 754 Single-Precision Float

Converting decimal numbers to IEEE 754 single-precision float is a common task in programming. Single-precision float is a binary format that is used to represent floating-point numbers. The format consists of a sign bit, an exponent, and a mantissa. To convert a decimal number to IEEE 754 single-precision float, follow these steps:

Índice
  1. Step 1: Convert the decimal number to binary
  2. Step 2: Normalize the binary number
  3. Step 3: Determine the sign bit
  4. Step 4: Convert the exponent to binary
  5. Step 5: Combine the sign bit, exponent, and mantissa

Step 1: Convert the decimal number to binary

Convert the decimal number to binary using the standard binary conversion method. For example, let's convert the decimal number 12.5 to binary:


12 / 2 = 6 remainder 0
 6 / 2 = 3 remainder 0
 3 / 2 = 1 remainder 1
 1 / 2 = 0 remainder 1

The binary representation of 12.5 is 1100.1.

Step 2: Normalize the binary number

Normalize the binary number by moving the decimal point to the left until there is only one digit to the left of the decimal point. Count the number of places you moved the decimal point, and subtract that number from the exponent. For example:


1.1001 × 2^3

In this example, we moved the decimal point three places to the left, so we subtract 3 from the exponent.

Step 3: Determine the sign bit

If the decimal number is positive, the sign bit is 0. If the decimal number is negative, the sign bit is 1.

Step 4: Convert the exponent to binary

Add the bias to the exponent and convert the sum to binary. The bias for single-precision float is 127. For example, if the exponent is -3:


-3 + 127 = 124
124 = 01111100

Step 5: Combine the sign bit, exponent, and mantissa

Combine the sign bit, exponent, and mantissa to form the final IEEE 754 single-precision float. The format is:


sign bit | exponent | mantissa

For example, if the decimal number is 12.5:


sign bit = 0 (positive)
exponent = 127 - 3 = 124 = 01111100
mantissa = 10010000000000000000000 (from step 2)

The final IEEE 754 single-precision float is:


0 01111100 10010000000000000000000

This is the binary representation of the decimal number 12.5 in IEEE 754 single-precision float format.

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