Binary Number Data Type

Signed vs. Unsigned Numbers

Was also learning more about this at Ericsson.

• In a signed representation, the largest number is $2^{n-1}-1$ . The next number after $2^{n-1}-1$ is $-2^{n-1}$ (the largest negative number)
  • I.e. go from $01111111$ (largest positive number) to $10000000$ (largest negative number)
• In an unsigned representation, the largest number is $2^n-1$. The next number after $2^n-1$ is $0$.
  • i.e. go from $11111111$ to $00000000$

Don’t believe me? The Source of Truth is code right. Consider the following code:

int x = 1 << 31 - 1; // LARGEST signed number
cout << x << "\n"; // 2147483647 
x++; 
cout << x << "\n"; // -2147483648
 
unsigned int x = (1 << 32) - 1; // Might give a warning, this is the largest unsigned number
cout << x << "\n"; // 4294967295 
x++; 
cout << x << "\n"; // 0

Notice that unsigned can give a bigger number because you have that additional bit that would otherwise be used to represent the negative sign for the signed numbers.

To understand how to read /write these signed numbers, see Complement.