The question asks to identify an invalid state within an 8-4-2-1 Binary Coded Decimal (BCD) counter. Let's break down what this means and analyze the options.

Understanding 8-4-2-1 BCD

8-4-2-1 BCD is a system where each decimal digit (0 through 9) is represented by a unique 4-bit binary code. The bits in each 4-bit group have positional weights: the leftmost bit has a weight of 8, the next bit has a weight of 4, the next has a weight of 2, and the rightmost bit has a weight of 1.

For a BCD code to be valid, the 4-bit combination must represent a decimal value between 0 and 9. Any 4-bit combination that results in a decimal value greater than 9 is considered an invalid BCD state.

Analyzing the Options

We will examine each option to see if it represents a valid decimal digit (0-9) according to the 8-4-2-1 weighting system.

Option 1: 1000

Let's calculate the decimal value:

Value = ($1 \times 8$) + ($0 \times 4$) + ($0 \times 2$) + ($0 \times 1$) = $8 + 0 + 0 + 0 = 8$

Since 8 is a valid decimal digit, 1000 is a valid 8-4-2-1 BCD code.

Option 2: 1001

Let's calculate the decimal value:

Value = ($1 \times 8$) + ($0 \times 4$) + ($0 \times 2$) + ($1 \times 1$) = $8 + 0 + 0 + 1 = 9$

Since 9 is a valid decimal digit, 1001 is a valid 8-4-2-1 BCD code.

Option 3: 0011

Let's calculate the decimal value:

Value = ($0 \times 8$) + ($0 \times 4$) + ($1 \times 2$) + ($1 \times 1$) = $0 + 0 + 2 + 1 = 3$

Since 3 is a valid decimal digit, 0011 is a valid 8-4-2-1 BCD code.

Option 4: 1100

Let's calculate the decimal value:

Value = ($1 \times 8$) + ($1 \times 4$) + ($0 \times 2$) + ($0 \times 1$) = $8 + 4 + 0 + 0 = 12$

The decimal value 12 is greater than 9. Therefore, 1100 is an invalid state in an 8-4-2-1 BCD counter.

Conclusion

Based on the analysis, the bit combination 1100 represents the decimal value 12, which is outside the range of 0-9 that standard BCD codes represent. Thus, it is an invalid state.