two’s complement arithmetic : Java Glossary

by Roedy Green ©1996-2008 Canadian Mind Products
Go to : punctuation 0-9 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z (all)

two’s complement arithmetic: Java internally uses (or emulates) two’s complement arithmetic. Positive numbers are stored in binary. That means that for example the number 13 would be written 0x0d = 00001101 = 1*8 + 1*4 + 0*2 + 1*1. The high order bit is called the sign bit. For signed quantities such as byte, short int and long, when that high order bit is a 1, we consider the number negative. To represent a negative number we first invert each bit, then add 1. We would write -13 this way: 0x0d - ⇒ 00001101 ⇒ 11110010 ⇒ 11110011 ⇒ 0xf3. Whenever you do any operation on a byte, it is first sign extended to an int. So so 13 ⇒ 0x0d ⇒ 00001101 ⇒ 00000000000000000000000000001101 ⇒ 0x0000000d and -13 ⇒ 0xf3 ⇒ 11110010 ⇒ 11111111111111111111111111110010 ⇒ 0xfffffff3. When you do arithmetic the results can be too big to represent. The arithmetic is done modulo 2 to the 32nd power, which is a fancy way of saying the high order bits of the result are discarded. The overflow may turn on the high order bit, making the result look negative. Don’t confuse two’s complement with two’s compliment an activity you do in the back seat of a car in an attempt to talk someone out of their clothes.
binary
one’s complement arithmetic
~

	Please email your feedback for publication, errors, omissions, broken/redirected link reports and suggestions to improve this page to Roedy Green :
	Canadian Mind Products
	mindprod.com IP:[65.110.21.43]
	Your face IP:[38.103.63.16]	The information on this page is for non-military use only.
	You are visitor number 18,591.	Military use includes use by defence contractors.
	You can get a fresh copy of this page from:	or possibly from your local J: drive (Java virtual drive/Mindprod website mirror)
	http://mindprod.com/jgloss/twoscomplement.html	J:\mindprod\jgloss\twoscomplement.html