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It is therefore the maximum value for variables declared as integers (e.g., as int) in many programming languages. The data type time_t, used on operating systems such as Unix, is a signed integer counting the number of seconds since the start of the Unix epoch (midnight UTC of 1 January 1970), and is often implemented as a 32-bit integer. [8]
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 ...
Two to the power of n, written as 2 n, is the number of values in which the bits in a binary word of length n can be set, where each bit is either of two values. A word, interpreted as representing an integer in a range starting at zero, referred to as an "unsigned integer", can represent values from 0 (000...000 2) to 2 n − 1 (111...111 2) inclusively.
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.
[1] [2] It follows 4,294,967,294 and precedes 4,294,967,296. It has a factorization of . In computing, 4,294,967,295 is the highest unsigned (that is, not negative) 32-bit integer, which makes it the highest possible number a 32-bit system can store in memory.
A natural number is a sociable narcissistic number if it is a periodic point for , where () = for a positive integer (here is the th iterate of ), and forms a cycle of period . A narcissistic number is a sociable narcissistic number with p = 1 {\displaystyle p=1} , and an amicable narcissistic number is a sociable narcissistic number with p = 2 ...
A natural number is a sociable Kaprekar number if it is a periodic point for ,, where , = for a positive integer (where , is the th iterate of ,), and forms a cycle of period . A Kaprekar number is a sociable Kaprekar number with k = 1 {\displaystyle k=1} , and a amicable Kaprekar number is a sociable Kaprekar number with k = 2 {\displaystyle k ...
A negative base (or negative radix) may be used to construct a non-standard positional numeral system.Like other place-value systems, each position holds multiples of the appropriate power of the system's base; but that base is negative—that is to say, the base b is equal to −r for some natural number r (r ≥ 2).