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A binary number is a number expressed in the base-2 ... [31] Later developments ... Stibitz was able to send the Complex Number Calculator remote commands over ...
In computing, signed number representations are required to encode negative numbers in binary number systems. In mathematics, negative numbers in any base are represented by prefixing them with a minus sign ("−"). However, in RAM or CPU registers, numbers are represented only as sequences of bits, without extra symbols.
A diagram showing how manipulating the least significant bits of a color can have a very subtle and generally unnoticeable effect on the color. In this diagram, green is represented by its RGB value, both in decimal and in binary. The red box surrounding the last two bits illustrates the least significant bits changed in the binary representation.
31 is the 11th prime number. It is a superprime and a self prime (after 3, 5, and 7), as no integer added up to its base 10 digits results in 31. [1] It is the third Mersenne prime of the form 2 n − 1, [2] and the eighth Mersenne prime exponent, [3] in-turn yielding the maximum positive value for a 32-bit signed binary integer in computing: 2,147,483,647.
Finger binary is a system for counting and displaying binary numbers on the fingers of either or both hands. Each finger represents one binary digit or bit . This allows counting from zero to 31 using the fingers of one hand, or 1023 using both: that is, up to 2 5 −1 or 2 10 −1 respectively.
As an example, consider the generator polynomial () = + + + + + +, chosen for use in the (31, 21) binary BCH code used by POCSAG and others. To encode the 21-bit message {101101110111101111101}, we first represent it as a polynomial over G F ( 2 ) {\displaystyle GF(2)} :
A bitwise AND is a binary operation that takes two equal-length binary representations and performs the logical AND operation on each pair of the corresponding bits. Thus, if both bits in the compared position are 1, the bit in the resulting binary representation is 1 (1 × 1 = 1); otherwise, the result is 0 (1 × 0 = 0 and 0 × 0 = 0).
The modern binary number system, the basis for binary code, is an invention by Gottfried Leibniz in 1689 and appears in his article Explication de l'Arithmétique Binaire (English: Explanation of the Binary Arithmetic) which uses only the characters 1 and 0, and some remarks on its usefulness. Leibniz's system uses 0 and 1, like the modern ...
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