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Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.
Logical shifts can be useful as efficient ways to perform multiplication or division of unsigned integers by powers of two. Shifting left by n bits on a signed or unsigned binary number has the effect of multiplying it by 2 n. Shifting right by n bits on an unsigned binary number has the effect of dividing it by 2 n (rounding towards 0).
It is just a representation of AND which does its work on the bits of the operands rather than the truth value of the operands. Bitwise binary AND performs logical conjunction (shown in the table above) of the bits in each position of a number in its binary form. For instance, working with a byte (the char type):
Shifting left by n bits on a signed or unsigned binary number has the effect of multiplying it by 2 n. Shifting right by n bits on a two's complement signed binary number has the effect of dividing it by 2 n, but it always rounds down (towards negative infinity). This is different from the way rounding is usually done in signed integer division ...
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).
While the exponent can be positive or negative, in binary formats it is stored as an unsigned number that has a fixed "bias" added to it. Values of all 0s in this field are reserved for the zeros and subnormal numbers; values of all 1s are reserved for the infinities and NaNs. The exponent range for normal numbers is [−126, 127] for single ...
A binary multiplier is an electronic circuit used in digital electronics, such as a computer, to multiply two binary numbers. A variety of computer arithmetic techniques can be used to implement a digital multiplier. Most techniques involve computing the set of partial products, which are then summed together using binary adders.
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 ...