[SOLVED] Cs211 digital logic assignment 2

1. (20 points 10+10) Simplify the following Boolean function F(A, B, C, D)= ∑(1, 2
, 4, 7, 8,
9, 11), together with the don’t-care conditions d(0, 3, 5), and express the simplified Boolean
function using （注意：表达式和电路图均需要，只有电路图将仅酌情得分）:
a) NAND gates only using algebraic method, and draw the logic diagram corresponding
to your function
b) NOR gates only using algebraic method, draw the logic diagram corresponding to your
function
2. (24 points 12+12) Obtain the simplified Boolean expressions for output F1 and F2 in terms
of the input variables in the following circuit.
a) Derive the Boolean expressions for T1 through T4. Evaluate the outputs F1 and F2 as a
function of the four inputs.
b) List the truth table of the four input variables. Then list the binary values for T1
through T4 and outputs F1 and F2 in the table.
3. (18 points 8+5+5) Design a combinational circuit with three inputs, A, B, and C, and three
outputs, F1, F2, and F3. When the binary input is 0, 1, or 2, the binary output is two greater
than the input. When the binary input is 3, 4, 5, 6, or 7, the binary output is one less than
the input. You need to provide:
a) List the truth table
b) K-map simplification
c) Draw the logic diagram
4. (18 points 6+6+6) A combinational circuit is defined by the equations
F1=AB+A’B’C’
F2=A+B+C’
F3=A’B+AB’
Design a circuit which implements these three equations using a decoder and NOR gates
external to the decoder, and draw the block diagram.
5. (20 points 8+6+6) An 8:1 multiplexer has inputs A, B, and C connected to the selection
inputs S2, S1, and S0, respectively. The data inputs I0 through I7 are as follows: I1=I2=0;
I3=I5=I7=1; I0=I4=D; and I6=D’. Determine the Boolean function F(A, B, C, D) that the
multiplexer implements. You need to:
a) Write down the truth table
b) Simplify the Boolean function with K-map
c) Redesign the circuit with ONLY 4:1 multiplexers