IEEE 754 Floating Point Converter

IEEE 754 is a standard for floating-point arithmetic used in computers. The format consists of three parts: sign bit, exponent, and mantissa (significand).

Format breakdown:

• 16-bit (Half Precision): 1 sign bit, 5 exponent bits (bias = 15), 10 mantissa bits. Range: ±65,504, Precision: ~3-4 decimal digits.
• 32-bit (Single Precision): 1 sign bit, 8 exponent bits (bias = 127), 23 mantissa bits. Range: ±3.4×10³⁸, Precision: ~7 decimal digits.
• 64-bit (Double Precision): 1 sign bit, 11 exponent bits (bias = 1023), 52 mantissa bits. Range: ±1.7×10³⁰⁸, Precision: ~15-17 decimal digits.

The value is calculated as: (-1)^sign × 2^(exponent - bias) × (1 + mantissa/2^mantissa_bits)

The value is calculated as: (-1)^sign × 2^(exponent - bias) × (1 + mantissa/2^mantissa_bits)

Examples:

• 16-bit example: Converting 3.5 to 16-bit. Binary: 0 10000 1100000000 (sign=0, exponent=16, mantissa=768). Value: 1 × 2^(16-15) × (1 + 768/1024) = 2 × 1.75 = 3.5
• 32-bit example: Converting 3.5 to 32-bit. Binary: 0 10000000 11000000000000000000000 (sign=0, exponent=128, mantissa=6291456). Value: 1 × 2^(128-127) × (1 + 6291456/8388608) = 2 × 1.75 = 3.5
• 64-bit example: Converting 3.5 to 64-bit. Binary: 0 10000000000 1100000000000000000000000000000000000000000000000000 (sign=0, exponent=1024, mantissa=3377699720527872). Value: 1 × 2^(1024-1023) × (1 + mantissa/2^52) = 2 × 1.75 = 3.5