Hexadecimal floating point literals

Question

How is 0x12.2P2 equal to 72.5?

I know that the value following P, called the binary exponent, indicates a power-two by which the number is multiplied?

Answer 1

0x12.2P2 - 0x122 / 16 ₁₀ * 2 ²

• 0x122 = 290 ₁₀
• divided by 16 ₁₀ = 18.125 ₁₀
• times 2 ² leads to 72.5 ₁₀

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More formally (?), For the part up to P , you can use this very classic conversion table:

  decimal point here ▼ +-----+-----+-----+-----+-+-----+-----+-----+ | 16³ | 16² | 16¹ | 16⁰ | | 16⁻¹| 16⁻²| 16⁻³| +-----------------------------------------+ | | | 1 | 2 |.| 2 | | | +-----+-----+-----+-----+-+-----+-----+-----+ 

Thus, 0x12.2 is 1⨯16¹ + 2x16⁰ + 2⨯16⁻¹ = 18.125