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In sum-of-products (SOP) form, AND gates form the smallest unit and are stitched together using ORs, whereas in product-of-sums (POS) form it is opposite. POS form requires parentheses to group the OR terms together under AND gates, because OR has lower precedence than AND. Both SOP and POS forms translate nicely into circuit logic.
CD4048B = single expandable 8-input 8-function with three-state output, 8 choices for gate type: 8 NOR / 8 OR / 8 NAND / 8 AND / 4-4 AND-OR-Invert / 4-4 AND-OR / 4-4 OR-AND-Invert / 4-4 OR-AND [7] TTL 7400-series logic family: (in past decades, a number of AOI parts were available in the 7400 family, but currently most are obsolete (no longer ...
The following 4-to-1 multiplexer is constructed from 3-state buffers and AND gates (the AND gates are acting as the decoder): A 4:1 MUX circuit using 3 input AND and other gates. The subscripts on the inputs indicate the decimal value of the binary control inputs at which that input is let through.
The very fastest shifters are implemented as full crossbars, in a manner similar to the 4-bit shifter depicted above, only larger. These incur the least delay, with the output always a single gate delay behind the input to be shifted (after allowing the small time needed for the shift count decoder to settle; this penalty, however, is only incurred when the shift count changes).
In Boolean algebra, any Boolean function can be expressed in the canonical disjunctive normal form , [1] minterm canonical form, or Sum of Products (SoP or SOP) as a disjunction (OR) of minterms. The De Morgan dual is the canonical conjunctive normal form ( CCNF ), maxterm canonical form , or Product of Sums ( PoS or POS ) which is a ...
These are functions, computed by restrict operator, (,,) and (,,) (see valuation (logic) and partial application). It has been called the "fundamental theorem of Boolean algebra". [ 1 ] Besides its theoretical importance, it paved the way for binary decision diagrams (BDDs), satisfiability solvers , and many other techniques relevant to ...
The advantages of a larger register file are offset by the need to use more bits to encode the register number. For instance, in a system using 32-bit instructions, you might wish to have three registers, such that you can perform operations of the type = +. If the register file contains 32 entries, each one of the references will require 5 ...
The adder–subtractor above could easily be extended to include more functions. For example, a 2-to-1 multiplexer could be introduced on each B i that would switch between zero and B i ; this could be used (in conjunction with D = 1 ) to yield the two's complement of A since − A = A + 1 .