Understanding Floating Point Mantissa (FP4)

FP4 format: 1 sign bit, 2 exponent bits (bias of 1), 1 mantissa bit

0.00

Decimal Value
Sign Bit
Positive
Exponent Bits
Bias of 1, Actual: -1
Mantissa Bit
Value: 0
-3 -2 -1 0 1 2 3
Slider value: 0 (adjusts sign & exponent only)

Binary Representation

0000 = 0 00 0

Explanation

Denormalized number: 1 × 2^(-1) × 0

The Role of the Mantissa

The mantissa represents the precision bits of a floating-point number.

In normalized form, the mantissa is interpreted as 1.mantissa_bits:

  • When mantissa bit = 0: value = 1.0
  • When mantissa bit = 1: value = 1.5

Try toggling the mantissa bit with exponent = 01 to see the value change between 1.0 and 1.5