Lesson 06: Combination Logic Circuits
6.6 Combinational Logic Circuit Design
The design procedure for combinational logic circuits starts with the problem specification and comprises the following steps:
- Determine the required number of inputs and outputs from the specifications.
- Derive the truth table for each output based on their relationships to the input.
- Simplify the boolean expression for each output. Use Karnaugh Maps or Boolean algebra.
- Draw a logic diagram that represents the simplified Boolean expression.
- Verify the design by analyzing or simulating the circuit.
5 or more
Design a circuit that has a 3-bit binary input and a single output (Z) specified as follows:
- Z = 0, when the input is less than (5)10
- Z = 1, otherwise
BCD to 7-Segment Decoder
Design a BCD to 7-segment decoder circuit for an seven-segment display that has a 4-bit binary input and seven output (seg-a, -b, -c, -d, -e, -f, and -g) specified by the truth table.
Odd Numbers
Design a circuit that has a 3-bit binary input B2, B1, and B0 (where B2 is MSB and B0 is LSB) and a single output (Z) specified as follows:
- Z = 0, even numbers
- Z = 1, odd numbers 1, 3, 5, 7
Bank Alarm System
A bank wants to install an alarm system with movement sensors. The bank has three sensors (A, B, C).
The alarm will be triggered only when at least two sensors activate simultaneously to prevent false alarms produced by a single sensor activation.
Car Safety Buzzer
Turn On the B(uzzer) whenever the D(oor) is Open OR when the K(ey) is in the Ignition AND the S(eat belt) is NOT Buckled. The logic values for each component are as below:
- 0 : Seat Belt is NOT Buckled
1 : Seat Belt is Buckled - 0 : Key is NOT in the Ignition
1 : Key is in the Ignition - 0 : Door is NOT Open
1 : Door is Open - 0 : Buzzer is OFF
1 : Buzzer is ON
Prime Numbers
Design a circuit that has a 3-bit binary input and a single output (Z) specified as follows:
- Z = 0, non prime number
- Z = 1, prime numbers 2, 3, 5, 7
1-bit Half Adder
The half-adder adds two one-bit binary numbers, A and B. The output is the Sum (S) of the two bits and the Carryout (Cout).
{Cout, S} = A + B
1-bit Full Adder
For a full adder, besides the two inputs bits A and B, the Carry in (Cin) bit is included. The outputs are Sum (S) and Carryout (Cout).
{Cout, S} = A + B + Cin
1-bit Half Subtractor
The half-subtractor subtracts two one-bit binary numbers, A and B. It produces the Difference (D) between the two input binary bits, and also produces an output Borrow (Bout) bit that indicates if one has been borrowed. In the subtraction (A - B), the A is called a Minuend bit, and the B is called a Subtrahend bit.
{Bout, D} = A - B
1-bit Full Subtractor
The half-subtractor has three inputs and two outputs. The inputs are A, B, and Bin, which denote the minuend, subtrahend, and previous borrow, respectively. The outputs are D and Bout, which re[resemt the difference and output borrow, respectively.
{Bout, D} = A - B - Bin