• Number 0
• Edge Case True
• Sign Bit 1
• Exponent Bits 5
• Mantissa Bits 10
• Total Bits 16
• Sign 0
• Scale
• Scaled Number
• Scaled Number In Binary
• Unable To Scale No
• Bias 15
• Bias In Binary 01111
• Exponent 00000
• Mantissa 0000000000
• Mantissa Base 10
• Result 0 00000 0000000000
• Hexadecimal 0000
• Hexadecimal Parts 0000 0000 0000 0000
• Converted Number
• Error

• Sign bit is either 0 or 1 for positive and negative numbers, respectively

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0 > 0 → 0

Sign = 0

• Multiply the number by 2
• Repeat until the number is an integer
• Count the number of multiplications
• Save the integer number for later use

• Find the minimum and maximum exponent
• Leave the minimum exponent for later use
• Leave the maximum exponent for later use
• Count the possible exponent values between the minimum and maximum
• Divide the possible exponent values by 2
• Get the middle value as the bias

or
Use the following formula to calculate the bias directly:

↓

Bias = 2^{Number of Exponent Bits - 1} - 1

Bias = 2^{5 - 1} - 1 = 2⁴ - 1 = 16 - 1

Bias = 15

• Convert the scaled up number to binary
• Normalize the binary number by leaving only one digit before the decimal point
• Count the number of digits after the decimal point
• Exponent is the sum of this count and the bias subtracted by the scale
• Convert the sum to binary
• Truncate the result to the desired precision
• Pad the result with 0s to the desired precision

Exponent = 00000

• Convert the scaled up number to binary
• Normalize the binary number by leaving only one digit before the decimal point
• The mantissa is the fraction part of the normalized binary number
• Truncate the result to the desired precision
• Round up the last digit to 1 if the number is truncated
• Pad the result with 0s to the desired precision

---

Mantissa = 0000000000

• Sign Bit 0
• Exponent Bits 00000
• Mantissa Bits 0000000000

• 0 00000 0000000000

• Complete the length of bits to a multiple of 4 by padding 0s to the left if necessary
• Split the bits to include 4 digits in each group
• Convert each group to hexadecimal

---

0000 0000 0000 0000

0 0 0 0

Hex: 0000

• Convert the IEEE 754 representation back to float
• Calculate the error by subtracting the converted number from the original number