Why Does fmt.Printf Output \'-101\' When Printing a Binary Representation of a Signed Integer in Go?

Two's Complement and the Puzzling Output of fmt.Printf

In the realm of computer science, Two's complement is the prevalent method employed to represent signed integers internally. This representation involves flipping the bits and adding one to express negative numbers. For instance, in Two's complement, -5 would be represented in binary format as "1111 1011" (equivalent to ^5 1).

A perplexity arises when attempting to print a signed integer's binary representation using fmt.Printf. Consider the following code snippet:

var i int8 = -5
fmt.Printf("%b", i)

Expectedly, this code should output "1111 1011," the Two's complement representation of -5. However, the actual output is "-101," which deviates from this expectation. This raises the question: is the value internally stored in Two's complement format, or is a different representation being used?

Intriguingly, converting the value to an unsigned integer before printing it yields the desired result:

var u uint8 = uint(i)
fmt.Printf("%b", u)

This results in an output of "11111011," the exact Two's complement representation of -5.

The crux of the discrepancy lies in how fmt.Printf handles the formatting of binary numbers. Upon closer inspection of the fmt.integer function, it becomes clear that the negative signed integer is converted to a positive one during the formatting process:

   165      negative := signedness == signed && a <p>This conversion necessitates the addition of a '-' prefix to the formatted string, which explains the "-101" output observed earlier.</p><p>In essence, the internal representation of the value adheres to the Two's complement convention, while the formatting process in fmt.integer converts the negative signed integer to its positive counterpart, leading to the unexpected output.</p>

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