The OR gate is a digital logic gate that implements logical disjunction – it behaves according to the truth table to the right. A HIGH output (1) results if one or both the inputs to the gate are HIGH (1). If neither input is HIGH, a LOW output (0) results. The expression X = A …
XOR (Exclusive OR) Gate The XOR gate (sometimes EOR gate) is a digital logic gate that implements exclusive disjunction – it behaves according to the truth table to the right. A HIGH output (1) results if one, and only one, of the inputs to the gate is HIGH (1). If both inputs are LOW (0) …
A truth table is a mathematical table used in logic — specifically in connection with Boolean algebra, Boolean functions, and propositional calculus — to compute the functional values of logical expressions on each of their functional arguments, that is, on each combination of values taken by their logical variables. In particular, truth tables can be used to …
Logic Gates Timing Diagram The operation of a logic gate can also be represented with a timing diagram. Images below shows the output that results from three binary input signals for an AND gate, OR gate, and XOR gate respectively. Remember that the AND gate outputs a one only if all its inputs equal one, the OR gate outputs a one if any input equals …
Boolean algebra (or Boolean logic) is a logical calculus of truth values, developed by George Boole. It resembles the algebra of real numbers as taught in high school, but with the numeric operations of multiplication xy, addition x + y, and negation -x replaced, respectively, by the logical operations of conjunction x?y, disjunction x?y, and …
Boolean algebra Symbols Analogous behavior can be shown between Boolean algebra and mathematical algebra, and as a result, similar symbols and syntax can be used. For example, the following expressions hold true in math. This looks like the AND function allowing an analogy to be drawn between the mathematical multiply and the Boolean AND functions. …
Laws & Rules of Boolean algebra The manipulation of algebraic expressions is based on fundamental laws. Some of these laws extend to the manipulation of Boolean expressions. For example, the commutative law of algebra which states th at the result of an operation is the same regardless of the order of operands holds true for Boolean algebra too. This is shown …
Adders Most mathematical operations can be handled with addition. For example, subtraction can be performed by taking the two’s complement of a binary value, and then adding it to the binary value from which it was to be subtracted. Two numbers can be multiplied using multiple additions. Counting either up or down (incrementing or decrementing) can be …
Multiplexers A multiplexer, sometimes referred to as a MUX, is a device that uses a set of control inputs to select which of several data inputs is to be connected to a single data output. With n binary “select lines,” one of 2n data inputs can be connected to the output. Image below presents a block diagram …
De-Multiplexers The previous section described how multiplexers select one channel from a group of input channels to be sent to a single output. Demultiplexers take a single input and select one channel out of a group of output channels to which it will route the input. It’s like having multiple printers connected to a computer. A document can only …