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Decoder • Is a combinational circuit that converts binary information from n input lines to a maximum of 2n unique output lines For example if the number of input is n=3 the number of output lines can be m=23 . It is also known as 1 of 8 because one output line is selected out of 8 available lines: 3 to 8 decoder enable
Decoder with Enable Line • Decoders usually have an enable line, • If enable=0 , decoder is off. It means all output lines are zero • If enable=1, decoder is on and depending on input, the corresponding output line is 1, all other lines are 0 • See the truth table in next slide
Major application of Decoder • Decoder is use to implement any combinational cicuits ( fn ) For example the truth table for full adder is s (x,y,z) = ∑ ( 1,2,4,7) and C(x,y,z)= ∑ (3,5,6,7). The implementation with decoder is:
Encoder • Encoder is a digital circuit that performs the inverse operation of a decoder • Generates a unique binary code from several input lines. • Generally encoders produce2-bit, 3-bit or 4-bit code. n bit encoder has 2n input lines 2 bit encoder
2-bit encoder • If one of the four input lines is active encoder produces the binary code corresponding to that line • If more than one of the input lines will be activated or all the output is undefined. We can consider don’t care for these situations but in general we can solve this problem by using priority encoder.
2-bit Priority Encoder • A priority encoder is an encoder circuit that includes priority function. • It means if two or more inputs are equal to 1 at the same time, the input having higher subscript number, considered as a higher priority. For example if D3 is 1 regardless of the value of the other input lines the result of output is 3 which is 11. • If all inputs are 0, there is no valid input. For detecting this situation we considered a third output named V. V is equal to 0 when all input are 0 and is one for rest of the situations of TT.
2-bit Priority Encoder • By using TT and K-map we get following Boolean functions for 4-input (or 2-bit) priority encoder: • X = D2 + D3 • Y = D3 + D1D’2 • V= D0 + D1 + D2 + D3 See next two slides for K-maps and the logic circuit of 2-bit priority encoder
Multiplexer • It is a combinational circuit that selects binary information from one of the input lines and directs it to a single output line • Usually there are 2n input lines and n selection lines whose bit combinations determine which input line is selected • For example for 2-to-1 multiplexer if selection S is zero then I0 has the path to output and if S is one I1 has the path to output (see the next slide)
Boolean function Implementation • Another method for implementing boolean function is using multiplexer • For doing that assume boolean function has n variables. We have to use multiplexer with n-1 selection lines and • 1- first n-1 variables of function is used for data input • 2- the remaining single variable ( named z )is used for data input. Each data input can be z, z’, 1 or 0. From truth table we have to find the relation of F and z to be able to design input lines. For example : f(x,y,z) = ∑(1,2,6,7)
8-to-1 Multiplexer F A,B,C,D = ∑(1,3,4,11,12,13,14,15)
Three-State Gates • Three state gates exhibit three states instead of two states. The three states are: • high : 1 • Low : 0 • High impedance : In that state the output is disconnected which is equal to open circuit. In the other words in that state circuit has no logic significant. We can have AND or NAND tree-state gates but the most common is three-state buffer gate
Three-State Gates • We may use conventional gates such as AND or NAND as tree-state gates but the most common is three-state buffer gate. • Note that buffer produces transfer function and can be used for power amplification. Three state buffer has extra input control line entering the bottom of the gate symbol (see next slide)
Three-state buffer • C A Y • ---------------------- • 0 0 z • 0 1 z • 0 0 • 1 1 1
