represent negative number with 2' complement technique?

Question

I am using 2' complement to represent a negative number in binary form

Case 1:number -5

According to the 2' complement technique:

Convert 5 to the binary form:

00000101, then flip the bits

11111010, then add 1

00000001

=> result: 11111011

To make sure this is correct, I re-calculate to decimal:

-128 + 64 + 32 + 16 + 8 + 2 + 1 = -5

Case 2: number -240

The same steps are taken:

11110000 00001111 00000001 00010000 => recalculate this I got 16, not -240

I am misunderstanding something?

MA Xilai · Accepted Answer · 2017-05-09 05:19:34Z

The problem is that you are trying to represent 240 with only 8 bits. The range of an 8 bit signed number is -128 to 127.

If you instead represent it with 9 bits, you'll see you get the correct answer:

011110000 (240) 100001111 (flip the signs) + 000000001 (1) = 100010000 = -256 + 16 = -240

prajeesh kumar · Accepted Answer · 2012-02-07 06:57:16Z

4

Did you forget that -240 cannot be represented with 8 bits when it is signed ?

answered Feb 7, 2012 at 6:57

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Comments

Ateş Göral · Accepted Answer · 2012-02-07 07:01:22Z

The lowest negative number you can express with 8 bits is -128, which is 10000000.

Using 2's complement:

 128 = 10000000 (flip) = 01111111 (add 1) = 10000000

The lowest negative number you can express with N bits (with signed integers of course) is always - 2 ^ (N - 1).