Design a BCD to excess-3 code converter. Design a MOD-5 counter.

Design a BCD to Excess-3 Code Converter

A BCD (Binary-Coded Decimal) to Excess-3 code converter is a digital circuit that converts a BCD number into its corresponding Excess-3 code. Excess-3 is a non-weighted code used to express decimal numbers. It is obtained by adding 3 to each digit of the BCD representation.

Step-by-Step Approach:

1. Understand the BCD and Excess-3 Codes:

   • BCD represents each decimal digit in its four-bit binary form.
   • Excess-3 code is a self-complementary BCD code and is obtained by adding 3 to the BCD representation.

2. Create the Truth Table:

   • List all possible combinations of BCD inputs and their corresponding Excess-3 outputs.

BCD Input	Excess-3 Output
0000	0011
0001	0100
0010	0101
0011	0110
0100	0111
0101	1000
0110	1001
0111	1010
1000	1011
1001	1100

1. Determine the Logic Expressions:

   • Using Karnaugh maps or Boolean algebra, derive the logic expressions for each output bit (D, C, B, A) based on the BCD inputs (D3, D2, D1, D0).

2. Draw the Logic Circuit:

   • Use the logic expressions to create the circuit with logic gates.

Example:

Let's derive the logic expressions for a 4-bit BCD to Excess-3 converter.

• For the Excess-3 output bit D (MSB):
  • D = D3
• For the Excess-3 output bit C:
  • C = D2 + (D1 * D0)
• For the Excess-3 output bit B:
  • B = D1' * D0 + D1 * D0'
• For the Excess-3 output bit A (LSB):
  • A = D0'

Using these expressions, we can draw the logic circuit with AND, OR, and NOT gates.

Design a MOD-5 Counter

A MOD-5 counter is a digital counter that counts from 0 to 4 and then resets to 0. It has 5 states in total.

Step-by-Step Approach:

1. Understand the MOD-5 Counter:

   • A MOD-5 counter has 5 states (0 to 4) and then repeats.

2. Create the State Diagram:

   • Draw a state diagram that shows the sequence of states and transitions.

3. Create the Truth Table:

   • List the present state and next state for the counter.

Present State (Q1 Q0)	Next State (Q1+ Q0+)
00	01
01	10
10	11
11	00
00	01

1. Determine the Flip-Flop Inputs:

   • Choose the type of flip-flop (e.g., JK, D, T) and determine the inputs required to achieve the state transitions.

2. Draw the Logic Circuit:

   • Use the determined flip-flop inputs to create the circuit.

Example:

Let's design a MOD-5 counter using JK flip-flops.

• For the flip-flop Q0:
  • J0 = K0 = Q1'
• For the flip-flop Q1:
  • J1 = K1 = Q0

Using these expressions, we can draw the logic circuit with JK flip-flops and the necessary logic gates to provide the J and K inputs.

The MOD-5 counter will have a reset input to reset the counter to 0 when it reaches the count of 4 (binary 100). This can be achieved by using an AND gate that detects the state 100 and feeds it back as a reset signal.

In summary, designing a BCD to Excess-3 code converter and a MOD-5 counter involves understanding the codes/count sequences, creating truth tables, deriving logic expressions, and then constructing the logic circuit with the appropriate gates and flip-flops.