What is the difference between `bitCount()` and `bitLength()` of a `BigInteger`

Question

The descriptions of bitCount() and bitLength() are rather cryptic:

public int bitCount()

Returns the number of bits in the two's complement representation of this BigInteger that differ from its sign bit. This method is useful when implementing bit-vector style sets atop BigIntegers.

Returns: number of bits in the two's complement representation of this BigInteger that differ from its sign bit.

---

public int bitLength()

Returns the number of bits in the minimal two's-complement representation of this BigInteger, excluding a sign bit. For positive BigIntegers, this is equivalent to the number of bits in the ordinary binary representation. (Computes (ceil(log2(this < 0 ? -this : this+1))).)

Returns: number of bits in the minimal two's-complement representation of this BigInteger, excluding a sign bit.

What is the real difference between these two methods and when should I use which?

I have used bitCount occasionally to count the number of set bits in a positive integer but I've only rarely use bitLength and usually when I meant bitCount because the differences between the descriptions are too subtle for me to instantly grok.

Google Attractor: Java BigInteger bitCount vs bitLength

Answer 1

A quick demonstration:

public void test() {
    BigInteger b = BigInteger.valueOf(0x12345L);
    System.out.println("b = " + b.toString(2));
    System.out.println("bitCount(b) = " + b.bitCount());
    System.out.println("bitLength(b) = " + b.bitLength());
}

prints

b = 10010001101000101

bitCount(b) = 7

bitLength(b) = 17

So, for positive integers:

bitCount() returns the number of set bits in the number.

bitLength() returns the position of the highest set bit i.e. the length of the binary representation of the number (i.e. log₂).