Java - Bitwise operations not getting what expected

Question

private void test2() {
    // This test takes two shorts and sticks them together in a
    // 4 bit 12 bit configuration within a short, it then breaks
    // them apart again to see if it worked!
    short s0 = 4095;
    short s1 = 13;

    short sh = (short)((s1 << 12) | s0);

    System.out.println(sh);

    short[] sa = new short[] {
        (short)(sh & 0xFFF),
        (short)((sh >>> 12) & 0xF)
    };

    System.out.println(sa[0]);
    System.out.println(sa[1]);

}

What I expect from this is this;

s0 in binary is b0000_1111_1111_1111

s1 in binary is b0000_0000_0000_1101

sh then becomes b1101_1111_1111_1111

The preceeding 1 is the sign and the remaining 15 bits gives the value so sh in decimal is -24575 but this is not what I get outputted to the console (which is -8193).

What am I getting wrong?

Jochen · Accepted Answer · 2012-05-25 19:20:13Z

6

The result is actually correct. Binary numbers are represents in what is called the 2s-complement. So to compute the absolute value of a negative number, you do not just remove the sign bit and see what remains. Rather you do this: 1. Flip all bits, including the sign bit 2. Add 1

In your case that means you get

0010_0000_0000_0000
0010_0000_0000_0001

Which is 8193, which is exactly what is printed out.

edited May 25, 2012 at 19:20

answered May 25, 2012 at 19:07

Jochen

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1 Comment

Neilos Over a year ago

I see, thanks for the explanation, I'll do some reading on the matter =)

Kevin DiTraglia · Accepted Answer · 2012-05-25 19:06:39Z

6

b1101_1111_1111_1111 is -8193, it is outputting the correct answer. Might want to brush up on your 2s complements.

http://en.wikipedia.org/wiki/Two%27s_complement

answered May 25, 2012 at 19:06

Kevin DiTraglia

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5 Comments

Neilos Over a year ago

My bad, I'm a Physics grad not Computer Science, thanks for your response.

Neilos Over a year ago

indeed! There must be a reason for using 2s complements but at first glance it seems like the wrong choice lol! Thanks again.

Kevin DiTraglia Over a year ago

Well think about how a computer sees it. If you subtract 1 from 0, you expect to get -1, but it would actually end up being 1111111... which would be the max negative int how you displayed it, but it is negative 1 as 2s complement.

rlinden Over a year ago

The reason for using 2s-complement is because of the hardware implementation - when you use them, the computer can perform substractions with the same hardware it performs additions and no special treatment is necessary.

Neilos Over a year ago

I'm just reading that wiki page and it seems that there are lots of advantages over the way I thought it worked, which I think is 1s complement. It's just one of those non-intuitive things that we must come to accept I suppose! Quantum mechanics confused me in the beginning but now it is the only way I can see the world; curse you Newton I believed in you!

rlinden · Accepted Answer · 2012-05-25 19:08:34Z

2

The representation used is not sign-modulus, but yet 2-complement. Therefore, in order to know which number is represented by a sequence of bits that starts with one, you must subtract 1 and then invert. In your case you will get 1101_1111_1111_1110 inverted which will give 0010_0000_0000_0001 which is exatcly 8193. Therefore, there is no problem whatsoever - you just confused the nternal representation mechanism.

answered May 25, 2012 at 19:08

rlinden

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