FLOATING-POINT IN BINARY?

FLOATING POINT STANDARD:

• Defined by IEEE Std 754-1985
• Developed in response to divergence of representations
• Portability issues for scientific code
• Now almost universally adopted
• Two representations
• Single precision (32-bit)
• Double precision (64-bit)

S: sign bit (0 => non-negative, 1 => negative)
Normalize significand: 1.0 ≤ |significand| < 2.0

• Significand is Fraction with the “1.” restored
• Always has a leading pre-binary-point 1 bit, so no need to represent it explicitly (hidden bit)

Exponent: excess representation: actual exponent + Bias

• Ensures exponent is unsigned
• Single precision: Bias = 127;
• Double precision: Bias = 1203 

FOR MORE DETAILS CLICK HERE