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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 ...
Also, when the sum of two excess-3 digits is greater than 9, the carry bit of a 4-bit adder will be set high. This works because, after adding two digits, an "excess" value of 6 results in the sum. Because a 4-bit integer can only hold values 0 to 15, an excess of 6 means that any sum over 9 will overflow (produce a carry-out).
This scheme can also be referred to as Simple Binary-Coded Decimal (SBCD) or BCD 8421, and is the most common encoding. [12] Others include the so-called "4221" and "7421" encoding – named after the weighting used for the bits – and "Excess-3". [13]
One way to increment a Gray code number is to convert it into ordinary binary code, [55] add one to it with a standard binary adder, and then convert the result back to Gray code. [56] Other methods of counting in Gray code are discussed in a report by Robert W. Doran , including taking the output from the first latches of the master-slave flip ...
The IEEE 754 floating-point standard defines the exponent field of a single-precision (32-bit) number as an 8-bit excess-127 field. The double-precision (64-bit) exponent field is an 11-bit excess-1023 field; see exponent bias. It also had use for binary-coded decimal numbers as excess-3.
A truth table is a structured representation that presents all possible combinations of truth values for the input variables of a Boolean function and their corresponding output values. A function f from A to F is a special relation , a subset of A×F, which simply means that f can be listed as a list of input-output pairs.
3 triple 3-input expander for 74x52 14 SN74H61: 74x62 1 3-3-2-2-input AND-OR expander for 74x50, 74x53, 74x55 14 SN74H62: 74x63 6 hex current sensing interface gates 14 SN74LS63: 74x64 1 4-3-2-2-input AND-OR-Invert gate 14 SN74S64: 74x65 1 4-3-2-2 input AND-OR-Invert gate open-collector 14 SN74S65: 74x67 1
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: