Designing a SOP Circuit to Detect Decimal Numbers in a 4-bit 5211 BCD Code Input

Introduction:
In this task, we are required to design a SOP (Sum of Products) circuit that can detect the decimal numbers 0, 2, 4, 6, and 8 in a 4-bit 5211 BCD (Binary-Coded Decimal) code input. The BCD code is a coding scheme that represents each decimal digit with a four-bit binary number.

BCD Code:
The BCD code represents decimal numbers from 0 to 9 using four bits. In the 5211 BCD code, the four-bit representation for each decimal digit is as follows:
- Decimal 0: 0100
- Decimal 1: 0001
- Decimal 2: 0101
- Decimal 3: 0011
- Decimal 4: 0110
- Decimal 5: 0111
- Decimal 6: 1010
- Decimal 7: 1000
- Decimal 8: 1011
- Decimal 9: 1100

Designing the SOP Circuit:
To detect the decimal numbers 0, 2, 4, 6, and 8 in a 4-bit 5211 BCD code input, we can use a combination of AND and OR gates. Let's break down the design into steps:

Step 1: Input Variables:
We have a 4-bit input, which we can represent as A3, A2, A1, and A0. Each input represents a binary digit.

Step 2: Creating the SOP Expressions:
To detect the desired decimal numbers, we need to create SOP expressions for each number. The SOP expressions can be derived by analyzing the BCD code representation for each decimal number.

Decimal 0:
The BCD code representation for decimal 0 is 0100. To detect decimal 0, we need to check if A3 is 0, A2 is 1, A1 is 0, and A0 is 0. The corresponding SOP expression is:
- SOP_0 = A3' · A2 · A1' · A0'

Decimal 2:
The BCD code representation for decimal 2 is 0101. To detect decimal 2, we need to check if A3 is 0, A2 is 1, A1 is 0, and A0 is 1. The corresponding SOP expression is:
- SOP_2 = A3' · A2 · A1' · A0

Decimal 4:
The BCD code representation for decimal 4 is 0110. To detect decimal 4, we need to check if A3 is 0, A2 is 1, A1 is 1, and A0 is 0. The corresponding SOP expression is:
- SOP_4 = A3' · A2 · A1 · A0'

Decimal 6:
The BCD code representation for decimal 6 is 1010. To detect decimal 6, we need to check if A3 is 1, A2 is 0, A1 is 1