Instead of Exponent, think of a Window between two consecutive power of two integers. Instead of a Mantissa, think of an Offset within that window. - Floating point visually explained

• Float Exposed / HN
• Floating point from scratch: Hard Mode / HN - logic cells, hardware pipeline architectures, RTL (register-transfer level), ASIC floorplans, and tapeout. Building hardware is hard, as iteration cycles are long and fabricating stuff costs real money. That was quite a journey.

But why did DEC use 8 bits for the exponent in the F and D formats? The reason is to be able to represent all important physical constants, including the Plank constant (6.626070040 × 10^-34) and the Avogradro constant (6.022140857 × 10^23) - SO

see also

• Floating-point arithmetic (wikipedia)
• floats, bits, and constant expressions - Can you access the bits that represent an IEEE754 single precision float in a C++14 constant expression (constexpr)?
• The number of floats between 0 and 1
• C++ to machine code - C++ code snippet that we will compile defines two public functions, get_exponent() and set_exponent() - match 2 asm instruction when compiled.
• Posit floating point numbers: thin triangles and other tricks (2019 / HN