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Boolean logic allows 2 2 = 4 unary operators; the addition of a third value in ternary logic leads to a total of 3 3 = 27 distinct operators on a single input value. (This may be made clear by considering all possible truth tables for an arbitrary unary operator.
A truth table has one column for each input variable (for example, A and B), and one final column showing all of the possible results of the logical operation that the table represents (for example, A XOR B). Each row of the truth table contains one possible configuration of the input variables (for instance, A=true, B=false), and the result of ...
An input-consuming logic gate L is reversible if it meets the following conditions: (1) L(x) = y is a gate where for any output y, there is a unique input x; (2) The gate L is reversible if there is a gate L´(y) = x which maps y to x, for all y. An example of a reversible logic gate is a NOT, which can be described from its truth table below:
The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [ 1 ] and the LaTeX symbol.
The standard 4000 series CMOS IC is the 4071, which includes four independent two-input OR gates. The TTL device is the 7432. The TTL device is the 7432. There are many offshoots of the original 7432 OR gate, all having the same pinout but different internal architecture, allowing them to operate in different voltage ranges and/or at higher speeds.
Real world examples of an 3-3 AOI gate is found in the SN74LS51 logic IC (see further below). [5] The 3-3 AOI gate can be represented by the following boolean equation and truth table: = () ¯. Its logic table would have 64 entries, but is not shown.
The basic Fredkin gate [3] is a controlled swap gate (CSWAP gate) that maps three inputs (C, I 1, I 2) onto three outputs (C, O 1, O 2). The C input is mapped directly to the C output. If C = 0, no swap is performed; I 1 maps to O 1, and I 2 maps to O 2. Otherwise, the two outputs are swapped so that I 1 maps to O 2, and I 2 maps to O 1. It is ...
For example, a 4-to-2 simple encoder takes 4 input bits and produces 2 output bits. The illustrated gate level example implements the simple encoder defined by the truth table, but it must be understood that for all the non-explicitly defined input combinations (i.e., inputs containing 0, 2, 3, or 4 high bits) the outputs are treated as don't ...