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An asynchronous (ripple) counter is a "chain" of toggle (T) flip-flops in which the least-significant flip-flop (bit 0) is clocked by an external signal (the counter input clock), and all other flip-flops are clocked by the output of the nearest, less significant flip-flop (e.g., bit 0 clocks the bit 1 flip-flop, bit 1 clocks the bit 2 flip ...
A full adder can be viewed as a 3:2 lossy compressor: it sums three one-bit inputs and returns the result as a single two-bit number; that is, it maps 8 input values to 4 output values. (the term "compressor" instead of "counter" was introduced in [13])Thus, for example, a binary input of 101 results in an output of 1 + 0 + 1 = 10 (decimal ...
Breaking this down into more specific terms, in order to build a 4-bit carry-bypass adder, 6 full adders would be needed. The input buses would be a 4-bit A and a 4-bit B, with a carry-in (CIN) signal. The output would be a 4-bit bus X and a carry-out signal (COUT). The first two full adders would add the first two bits together.
A carry-save adder [1] [2] [nb 1] is a type of digital adder, used to efficiently compute the sum of three or more binary numbers. It differs from other digital adders in that it outputs two (or more) numbers, and the answer of the original summation can be achieved by adding these outputs together.
A 4-bit ripple-carry adder–subtractor based on a 4-bit adder that performs two's complement on A when D = 1 to yield S = B − A. Having an n-bit adder for A and B, then S = A + B. Then, assume the numbers are in two's complement. Then to perform B − A, two's complement theory says to invert each bit of A with a NOT gate then add one.
Sometimes a slightly different definition of propagate is used. By this definition A + B is said to propagate if the addition will carry whenever there is an input carry, but will not carry if there is no input carry. Due to the way generate and propagate bits are used by the carry-lookahead logic, it doesn't matter which definition is used.
For n = 3 the ternary median operator can be expressed using conjunction and disjunction as xy + yz + zx. For an arbitrary n there exists a monotone formula for majority of size O(n 5.3). This is proved using probabilistic method. Thus, this formula is non-constructive. [3] Approaches exist for an explicit formula for majority of polynomial size:
Ternary computing is commonly implemented in terms of balanced ternary, which uses the three digits −1, 0, and +1. The negative value of any balanced ternary digit can be obtained by replacing every + with a − and vice versa. It is easy to subtract a number by inverting the + and − digits and then using normal addition.