Digital Logic Design - Lecture 17: Problems (Mano)

DLDLecture 17Problems (Mano)Three-state gatesA multiplexer can be constructed with three-state gatesOutput state: 0, 1, and high-impedance (open ckts)If the select input (E) is 0, the three-state gate has no outputOpposite true here,No output if E is 1Three-State Buffers3-State buffer makes use of the output of two or more gates or other logic devices can be connected to each other.Enable Signal B = 1 the output C = AEnable Signal B = 0 the output C = OpenThree-State BuffersFour kinds of three-state buffersCan not operate: Output = ZUnclear output: Output = X(a)(b)(c)(d)Three-state gatesA multiplexer can be constructed with three-state gatesOutput state: 0, 1, and high-impedance (open ckts)If the Enable input is low, the three-state gate has no outputProblemDesign a 4-bit combinational circuit 2’s complementer (The output generates the 2’s complement of input binary number). Show that the circuit can be constructed using XOR gates. Can you predict what the output functions are for a 5-bit 2’s complementer?ProblemDesign a 4-bit combinational circuit 2’s complementer (The output generates the 2’s complement of input binary number). Show that the circuit can be constructed using XOR gates. Can you predict what the output functions are for a 5-bit 2’s complementer?ProblemDesign a 4-bit combinational circuit 2’s complementer (The output generates the 2’s complement of input binary number). Show that the circuit can be constructed using XOR gates. Can you predict what the output functions are for a 5-bit 2’s complementer?ProblemDesign a 4-bit combinational circuit 2’s complementer (The output generates the 2’s complement of input binary number). Show that the circuit can be constructed using XOR gates. Can you predict what the output functions are for a 5-bit 2’s complementer?ProblemDesign a 4-bit combinational circuit 2’s complementer (The output generates the 2’s complement of input binary number). Show that the circuit can be constructed using XOR gates. Can you predict what the output functions are for a 5-bit 2’s complementer?Try it yourselfProblemDesign a four-bit combinational circuit incrementer (a circuit that adds 1 to a four-bit binary number.(b) Design a four-bit combinational circuit decrementer (a circuit that subtracts 1 from a four bit binary number)Half AdderC A B S 0 0 0 1 A 0 B 0 S 0 C 1 0 0 0 00 1 1 01 0 1 01 1 0 1Dec Binary 1 1+1 +1 2 10Add two binary numbersA0 , B0 -> single bit inputsS0 -> single bit sumC1 -> carry outProblemDesign a four-bit combinational circuit incrementer (a circuit that adds 1 to a four-bit binary number.(b) Design a four-bit combinational circuit decrementer (a circuit that subtracts 1 from a four bit binary number)To decrement the 4-bit number, add -1 to the number. In 2's complement format ( add Fh ) to the number. An attempt to decrement 0 will assert the borrow bit.Full AdderSi = Ci (Ai Bi)Half-adderHalf-adderCi+1 = AiBi + Ci(Ai Bi)Full adder made of several half adders4-bit Subtractor: E = 1+1Add A to B’ (one’s complement) plus 1That is, add A to two’s complement of BD = A - BProblem (Mano)Design a combinational circuit that compares two four-bit numbers to check if they are equal. The circuit output is equal to 1 if the two numbers are equal and 0 otherwise.ProblemDraw the logic diagram of a two-to-four-line decoder using a NOR gates only including and enable input.Problem (Mano)Using a decoder and external gates, design the combinational circuit defined by the following three Boolean functions.ProblemUsing a decoder and external gates, design the combinational circuit defined by the following three Boolean functions.ProblemUsing a decoder and external gates, design the combinational circuit defined by the following three Boolean functions.ProblemUsing a decoder and external gates, design the combinational circuit defined by the following three Boolean functions.ProblemConstruct a 16 x1 multiplexer with two 8x1 and one 2 x 1 multiplexers. (Use Block Diagrams)ProblemImplement the following Boolean function with a 4 x 1 multiplexer and the external gatesProblemImplement the following Boolean function with a 4 x 1 multiplexer and the external gatesProblemAn 8 x 1 multiplexer has inputs A, B and C connected to the selection inputs S2, S1, S0 respectively. The data inputs I0 through I7 are as follows:ProblemAn 8 x 1 multiplexer has inputs A, B and C connected to the selection inputs S2, S1, S0 respectively. The data inputs I0 through I7 are as follows:SummaryMust solve as much problems as possibleTristate buffers have three types of outputs0, 1, high-impedence (Z)Useful for datapaths