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His first known work on binary, “On the Binary Progression", in 1679, Leibniz introduced conversion between decimal and binary, along with algorithms for performing basic arithmetic operations such as addition, subtraction, multiplication, and division using binary numbers. He also developed a form of binary algebra to calculate the square of ...
In some applications and programming languages, notably Microsoft Excel, PlanMaker (and other spreadsheet applications) and the programming language bc, unary operations have a higher priority than binary operations, that is, the unary minus has higher precedence than exponentiation, so in those languages −3 2 will be interpreted as (−3) 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 binary-reflected Gray code list for n bits can be generated recursively from the list for n − 1 bits by reflecting the list (i.e. listing the entries in reverse order), prefixing the entries in the original list with a binary 0, prefixing the entries in the reflected list with a binary 1, and then concatenating the original list with the ...
In a move or convert operation, zero extension refers to setting the high bits of the destination to zero, rather than setting them to a copy of the most significant bit of the source. If the source of the operation is an unsigned number, then zero extension is usually the correct way to move it to a larger field while preserving its numeric ...
In computer science, the double dabble algorithm is used to convert binary numbers into binary-coded decimal (BCD) notation. [ 1 ] [ 2 ] It is also known as the shift-and-add -3 algorithm , and can be implemented using a small number of gates in computer hardware, but at the expense of high latency .
For example, the sequence of powers of two (1, 2, 4, 8, ...), the basis of the binary numeral system, is a complete sequence; given any natural number, we can choose the values corresponding to the 1 bits in its binary representation and sum them to obtain that number (e.g. 37 = 100101 2 = 1 + 4 + 32). This sequence is minimal, since no value ...
The two basic types are the arithmetic left shift and the arithmetic right shift. For binary numbers it is a bitwise operation that shifts all of the bits of its operand; every bit in the operand is simply moved a given number of bit positions, and the vacant bit-positions are filled in.