Two's complement; 0FFFh positive, 0FFFFh negative?

2
votes

From the book, Art of Assembly, I copy this quote:

In the two’s complement system, the H.O. bit of a number is a sign bit. If the H.O. bit is zero, the number is positive; if the H.O. bit is one, the number is negative. Examples:

For 16-bit numbers:

8000h is negative because the H.O. bit is one.

100h is positive because the H.O. bit is zero.

7FFFh is positive.

0FFFFh is negative.

0FFFh is positive.

I don't understand the last two examples. If you convert the two examples to binary, you get 0000 1111 1111 1111 1111 for the first and 0000 1111 1111 1111 for the second. Why is the former negative and the latter positive? It seems to me that the highest order bit for both would be 0 and therefor both should be positive.

4
binaryx86twos-complement
in 16 bits, the conversion for those are 1111 1111 1111 1111 and 0000 1111 1111 1111. Your illustration shows 20 bits for the 0xffff. - gaige
ah. could you explain why 0FFFF has 5 digits? Is it the same as FFFF and if so is there a reason it is written as 0FFFF? - mage
Double-check the source. It's likely to say 0xffff, not 0ffff. The 0x indicates the number following it is in hex. - gaige
I copypasted directly, the h is used to indicate hex in this text. anyway, I suppose it is just the pdf I have and not convention then? - mage
nvmd, anakata answered it :) - mage

4 Answers

4
votes

The reason for the leading 0 on 0FFFFH is to give the assember/compiler a hint that F is part of a number. Not all assemblers require this.

So the negative number is in reality FFFFh, so 1111 1111 1111 1111, then is negative.

computer-programming-forum.com/46-asm/1b99282efbac3bcf.htm

1
votes

The text says: 16-bit numbers. So you need to look at the 16th bit from the right. In 0FFFF, that would be a 1. As for the leading zero, it's notational hint that the value is a number, not a word (i. e. not a variable).

Parsers (including assemblers) have easier time parsing numeric literals if you establish a convention that a valid number can only start with a digit. So do some humans. DEADBEEF is a valid hex number, y'know.

1
votes

could you explain why 0FFFF has 5 digits? Is it the same as FFFF

It is not the same. Just plain FFFFh will be interpreted as a symbol by the assembler. And you'll get a compile error since it cannot find any symbol named "FFFFh". Putting a 0 in front of it ensures that the assembler will interpret it as a number.

0
votes

if the number should be 16 bits, the 16th bit is taken as the sign bit. in the first,

0FFFFh

the 16th bit is 1 as it is

0000 1111 1111 1111 1111

in the second example,

0FFFh

the 16th bit is 0 as it is

0000 1111 1111 1111

the 16th bit is 0, though there are more than 16 digits, binary considers only the first 16 digits. so, the first is negative and the second is positive