Question

An AB latch operates as follows: If A = 0 and B = 0, the latch state is Q = 0; if either A = 1 or B = 1 (but not both), the latch output does not change; and when both A = 1 and B = 1, the latch state is Q = 1. (a) Construct the state table and derive the characteristic equation for this AB latch. (b) Derive a circuit for the AB latch that has four two-input NAND gates and two inverters. (c) In your circuit of part (b), are there any transitions between input combinations that might cause unreliable operation? Verify your answer.

(d) In your circuit of part (b), is there a gate output that provides the signal Q′? Verify your answer.
(e) Derive a circuit for the AB latch using four two-input NOR gates and two inverters. (f ) Answer parts (c) and (d) for your circuit of part (e).

Answer 1

The AB latch's state table and characteristic equation were derived according to given conditions. A theoretical NAND and NOR latch circuits were described with considerations for signal integrity and operations. A potential race condition could lead to unreliable operation, and the Q' output signal is provided directly in the NAND-based implementation.

Step-by-step explanation:

AB Latch State Table and Characteristic Equation

The state table for an AB latch based on the given conditions is:

• A=0, B=0, Q(next) = 0
• A=1, B=0, Q(next) = Q(previous)
• A=0, B=1, Q(next) = Q(previous)
• A=1, B=1, Q(next) = 1

To derive the characteristic equation, consider the conditions where Q does not change when A or B alone is 1, and Q becomes 1 only when both A and B are 1. This can be expressed as:

Q(next) = (A AND B) OR (NOT A AND NOT B AND Q(previous))

AB Latch Circuit with NAND Gates and Inverters

For constructing the AB latch using NAND gates and inverters, a feedback mechanism is necessary to hold the state. The following configuration can be used:

1. Connect a NAND gate to inputs A and B.
2. Connect the output of the first NAND gate to the inputs of the second NAND gate and connect one input of the third NAND gate.
3. Feed the output of the second NAND gate back into the second input of the third NAND gate and also one input of the fourth NAND gate.
4. Connect the output of the third NAND gate to one input of the first NAND gate.
5. The output of the fourth NAND gate is fed back to the other input of the first NAND gate and also serves as the inverse output, Q'.
6. Place inverters as needed to ensure correct logic levels at the feedback loops.

For the operation with NOR gates, follow a similar approach with NOR logic in place of NAND.

Transitions and Unreliable Operation

During transitions between input combinations, it is possible for an AB latch to experience unreliable operation if the inputs change near-simultaneously. This could result in a race condition, which would lead to an undefined output state due to the propagation delay inherent in the gates.

Output Signal Q'

For the constructed circuit with NAND gates, the output that provides the signal Q' is available from the output of the fourth NAND gate after one of the inputs is fed back from the output of the second NAND gate.

Answer 2

An AB latch operates based on certain input combinations, where the latch state and output change accordingly. The state table and characteristic equation can be derived for this latch. The circuit for the AB latch can be implemented using four two-input NAND gates and two inverters. It is important to consider potential transitions between input combinations that may cause unreliable operation. Furthermore, one of the NAND gate outputs provides the signal Q'. Alternatively, the AB latch circuit can be implemented using four two-input NOR gates and two inverters with no transitions that cause unreliable operation.

Step-by-step explanation:

For an AB latch, the state table and characteristic equation can be derived as follows:

a) State table:

ABQ00010Q01Q111

b) Circuit: The AB latch can be implemented using four two-input NAND gates and two inverters. The circuit is as follows:

See attached circuit diagram for visual representation.

AB Latch Circuit

A = 0, B = 0, Q = 0

• Connect A and B to the inputs of the first NAND gate.

• Connect A and B to the inputs of the second NAND gate.

• Connect the outputs of the first and second NAND gates to the inputs of the third NAND gate.

• Connect the output of the third NAND gate to the input of the fourth NAND gate.

• Connect the outputs of the second and fourth NAND gates to the inputs of the inverters.

• The outputs of the inverters are the Q and Q' outputs of the AB latch.

c) Yes, there are transitions between input combinations that might cause unreliable operation. When A = 1, B = 0 and A = 0, B = 1, the latch output may oscillate between 0 and 1 due to the rapid switching of inputs.

d) The gate output that provides the signal Q' is the output of the second NAND gate.

e) A circuit for the AB latch using four two-input NOR gates and two inverters can be derived as follows:

AB Latch Circuit Using NOR Gates

Use De Morgan's theorem to convert the NAND gate circuit to a NOR gate circuit.

• Connect A and B to the inputs of the first NOR gate.

• Connect A and B to the inputs of the second NOR gate.

• Connect the outputs of the first and second NOR gates to the inputs of the third NOR gate.

• Connect the output of the third NOR gate to the input of the fourth NOR gate.

• Connect the outputs of the second and fourth NOR gates to the inputs of the inverters.

• The outputs of the inverters are the Q and Q' outputs of the AB latch.

f) In the circuit using NOR gates, there are no transitions between input combinations that might cause unreliable operation. Each input combination leads to a unique and stable output.