Lecture Digital logic design - Lecture 17: Problems (Mano)

Lecture Digital logic design - Lecture 17: Problems (Mano). The following will be discussed in this chapter: Must solve as much problems as possible, tristate buffers have three types of outputs (0, 1, high-impedence (Z); useful for datapaths.)

DLD Lecture 17 Problems (Mano) Thr ee-• stat A multiplexer can be constructed with three-state gates e • Output state: 0, 1, and high-impedance (open ckts) gat• If the select input (E) is 0, the three-state gate has no es output Opposite true here, No output if E is Three-State Buffers ° 3-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 = the output C = A ° Enable Signal B = the output C = Open Three-State Buffers ° Four kinds of three-state buffers ° Can not operate: Output = Z Unclear output: Output = X (a) (b) (c) (d) Thr eestat• e • gat• es A multiplexer can be constructed with three-state gates Output state: 0, 1, and high-impedance (open ckts) If the Enable input is low, the three-state gate has no output Problem Design 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? Problem Design 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? Problem Design 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? Problem Design 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? Problem Design 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 yourself 10 Problem Design a four-bit combinational circuit incrementer (a circuit that adds to a four-bit binary number (b) Design a four-bit combinational circuit decrementer (a circuit that subtracts 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 will assert the borrow bit 13 Full Add ° Full er adder made of several half adders Si = Ci ⊕ (Ai ⊕ Bi) Ci+1 = AiBi + Ci(Ai ⊕ Bi) C i  A i  S i  B  i  Half­adder Half­adder C  i+1  14 4-bit Subtractor: E = A 3  B  3  A 2  B 2  A 1  B 1  A 0  B  0  E  Full Adder C  Full Adder 3  C 4  SD 3  SD 2  Full Adder C 2  Full Adder C 1  SD 1  +1 SD 0  Add A to B’ (one’s complement) plus 1 That is, add A to two’s complement of B D = A ­ B 15 Problem (Mano) Design a combinational circuit that compares two four-bit numbers to check if they are equal The circuit output is equal to if the two numbers are equal and otherwise 16 Problem Draw the logic diagram of a two-to-four-line decoder using a NOR gates only including and enable input 17 Problem (Mano) Using a decoder and external gates, design the combinational circuit defined by the following three Boolean functions 18 Problem Using a decoder and external gates, design the combinational circuit defined by the following three Boolean functions 19 Problem Using a decoder and external gates, design the combinational circuit defined by the following three Boolean functions 20 Problem Using a decoder and external gates, design the combinational circuit defined by the following three Boolean functions 21 Problem Construct a 16 x1 multiplexer with two 8x1 and one x multiplexers (Use Block Diagrams) 22 Problem Implement the following Boolean function with a x multiplexer and the external gates 23 Problem Implement the following Boolean function with a x multiplexer and the external gates 24 Problem An x 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: 25 Problem An x 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: 26 Summary ° Must solve as much problems as possible ° Tristate buffers have three types of outputs • 0, 1, high-impedence (Z) • Useful for datapaths 27 ... are for a 5-bit 2’s complementer? Try it yourself 10 Problem Design a four-bit combinational circuit incrementer (a circuit that adds to a four-bit binary number (b) Design a four-bit combinational... otherwise 16 Problem Draw the logic diagram of a two-to-four-line decoder using a NOR gates only including and enable input 17 Problem (Mano) Using a decoder and external gates, design the combinational... numbers • A0 , B0 -> single bit inputs • S0 -> single bit sum • C1 -> carry out A 0  B 0  A 0  B 0  S 0  C 1  0 1 1 1 0 0 S 0  C 1  Dec Binary +1 +1 10 12 Problem Design a four-bit combinational