How many 2-to-1 Multiplexers are required to construct an 8-to-1 Multiplexer?
To construct an N-to-1 MUX using 2-to-1 MUXes, total 2-to-1 MUXes required = N - 1. For N = 8, total MUXes = 8 - 1 = 7 (4 in stage 1, 2 in stage 2, 1 in final stage).
A Full Adder circuit can be constructed using which of the following combinations?
A Full Adder can be realized using 2 Half Adders and 1 OR gate. The first Half Adder adds A and B, the second Half Adder adds the sum output to Cin, and the OR gate combines the carry outputs.
What is the Boolean expression for the Carry output (C_{out}) of a Full Adder with inputs A, B, and $C_{in}$?
The Carry output of a Full Adder is given by C_{out} = AB + BC_in + AC_in (or AB + $C_{in}$(A ⊕ B)). It generates a carry whenever at least two of the three inputs are 1.
In a 4-to-1 Multiplexer with inputs I0, I1, I2, I3, if select lines are set to S1 = 1 and S0 = 0, which input line is selected at the output Y?
The select line binary combination (S1, S0) = (1, 0)_2 corresponds to decimal index 2. Therefore, input line I2 is selected and routed to output Y.
Which combinational logic circuit converts an n-bit binary code into a maximum of 2^n unique output lines?
A Decoder is a combinational circuit that converts an n-bit coded input into up to 2^n unique output lines, where exactly one output line is activated for each input combination.