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.)

1 Lecture 17

Problems (Mano)

Thr ee- stat

e gat es

• A multiplexer can be constructed with three-state gates

• Output state: 0, 1, and high-impedance (open ckts)

• If the select input (E) is 0, the three-state gate has no output

Opposite true here,

No output if E is 1

° 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 = 1 the output C = A

° Enable Signal B = 0 the output C = Open

Three-State Buffers

° Four kinds of three-state buffers

° Can not operate: Output = Z

Unclear output: Output = X

• 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?

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?

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

(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)

2 10

° Add two binary numbers

• A 0 , B 0 -> single bit inputs

• S 0 -> single bit sum

• C 1 -> carry out

(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.

17 Draw 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.

19 combinational circuit defined by the following three Boolean functions.

Problem

Using a decoder and external gates, design the

combinational circuit defined by the following three Boolean functions.

21 combinational circuit defined by the following three Boolean functions.

Problem

Construct a 16 x1 multiplexer with two 8x1 and one 2 x 1 multiplexers (Use Block Diagrams)

23 Implement the following Boolean function with a 4 x 1

multiplexer and the external gates

Problem

Implement the following Boolean function with a 4 x 1

multiplexer and the external gates

° Must solve as much problems as possible

° Tristate buffers have three types of outputs

• 0, 1, high-impedence (Z)

• Useful for datapaths