**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