How does `%b` represent float64 values in Go\'s `fmt.Printf`?

Understanding "%b" for Float64 in fmt.Printf

In the Go fmt package, %b for float64 in fmt.Printf represents the floating-point number in the binary format, specifically known as the [decimalless scientific notation](https://golang.org/pkg/fmt/#hdr-Printing). This notation uses a power of two exponent, similar to the 'b' format in strconv.FormatFloat.

Example:

fmt.Printf("0b%b\n", 255) // 0b11111111
fmt.Printf("%b\n", 1.0)   // 4503599627370496p-52

The output shows:

• 0b11111111: Binary representation of 255 (decimal).
• 4503599627370496p-52: Floating-point representation of 1.0 (decimal).

Breaking Down the Output for 1.0:

4503599627370496p-52 can be broken down as:

• 4503599627370496: Significand (the fractional part without the leading 1)
• p-52: Exponent (power of two)

Significand:

The significand represents the fractional part of the number, excluding the leading 1. In this case, it is 4503599627370496.

Exponent:

The exponent indicates the power of two by which the significand is multiplied to obtain the actual floating-point value. In this case, the exponent is -52, which means the significand is multiplied by 2^-52 to get the final value of 1.0.

Min Subnormal Positive Double in Float64

The minimum positive subnormal double in float64 is the smallest positive non-zero value that can be represented in this floating-point format. It is computed as:

Exp(2, -1022 - 52)

where Exp is the exponential function and 1022 is the bias value for float64. The result is an extremely small number close to, but not equal to, zero:

5e-324

This value is represented in binary as 0X0000000000000001.

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