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For example, a two's complement signed 16-bit integer can hold the values −32768 to 32767 inclusively, while an unsigned 16 bit integer can hold the values 0 to 65535. For this sign representation method, the leftmost bit ( most significant bit ) denotes whether the value is negative (0 for positive or zero, 1 for negative).
In computer science, an integer is a datum of integral data type, a data type that represents some range of mathematical integers. Integral data types may be of different sizes and may or may not be allowed to contain negative values. Integers are commonly represented in a computer as a group of binary digits (bits). The size of the grouping ...
Fixed length integer approximation data types (or subsets) are denoted int or Integer in several programming languages (such as Algol68, C, Java, Delphi, etc.). Variable-length representations of integers, such as bignums, can store any integer that fits in the computer's memory. Other integer data types are implemented with a fixed size ...
Binary integer formats can use various encodings. In the widely used two's complement encoding, zero is unsigned. In a 1+7-bit sign-and-magnitude representation for integers, negative zero is represented by the bit string 1000 0000. In an 8-bit ones' complement representation, negative zero is represented by the bit string 1111 1111.
Integer overflow can be demonstrated through an odometer overflowing, a mechanical version of the phenomenon. All digits are set to the maximum 9 and the next increment of the white digit causes a cascade of carry-over additions setting all digits to 0, but there is no higher digit (1,000,000s digit) to change to a 1, so the counter resets to zero.
Two's complement is the most common method of representing signed (positive, negative, and zero) integers on computers, [1] and more generally, fixed point binary values. Two's complement uses the binary digit with the greatest value as the sign to indicate whether the binary number is positive or negative; when the most significant bit is 1 the number is signed as negative and when the most ...
Negative zero behaves exactly like positive zero: when used as an operand in any calculation, the result will be the same whether an operand is positive or negative zero. The disadvantage is that the existence of two forms of the same value necessitates two comparisons when checking for equality with zero.
In Java, % is the remainder operator , and in Java, if its first operand is negative, the result can also be negative (unlike the modulo used in mathematics). Here, the programmer has assumed that total is non-negative, so that the remainder of a division with 2 will always be 0 or 1.