A 4 bit binary counter has reached the state 1001. What is the output after a further 7 clock cycles in binary. Answer with just 4 characters (eg 1010)

To determine the output of a 4-bit binary counter after a further 7 clock cycles from the state 1001, we can follow these steps:

1. Break Down the Problem

• Starting state: 1001 (in binary) which is 9 in decimal.
• We need to add 7 to this state.

2. Relevant Concepts

• A 4-bit binary counter can represent values from 0 (0000) to 15 (1111).
• Adding to the binary counter involves standard binary addition.

3. Analysis and Detail

1. Convert the binary number 1001 to decimal: $1001_2 = 1 \cdot 2^3 + 0 \cdot 2^2 + 0 \cdot 2^1 + 1 \cdot 2^0 = 8 + 1 = 9_{10}$

2. Add 7 to the decimal value: $9 + 7 = 16_{10}$

3. Since the counter is 4 bits, we need to convert 16 back to binary:

   • 16 is greater than the maximum representable value (15) in a 4-bit counter, so it wraps around: $16 \mod 16 = 0$

4. Convert 0 back to binary: $0_{10} = 0000_2$

4. Verify and Summarize

• After 7 clock cycles from 1001, the output wraps around and becomes 0000.

Final Answer

0000