1. **State the problem:** We need to subtract the base 4 number $13233_4$ from $32122_4$. 2. **Convert both numbers from base 4 to base 10:** - $32122_4 = 3 \times 4^4 + 2 \times 4^3 + 1 \times 4^2 + 2 \times 4^1 + 2 \times 4^0$ - Calculate powers: $4^4=256$, $4^3=64$, $4^2=16$, $4^1=4$, $4^0=1$ - Substitute: $3 \times 256 + 2 \times 64 + 1 \times 16 + 2 \times 4 + 2 \times 1 = 768 + 128 + 16 + 8 + 2 = 922$ - $13233_4 = 1 \times 4^4 + 3 \times 4^3 + 2 \times 4^2 + 3 \times 4^1 + 3 \times 4^0$ - Substitute: $1 \times 256 + 3 \times 64 + 2 \times 16 + 3 \times 4 + 3 \times 1 = 256 + 192 + 32 + 12 + 3 = 495$ 3. **Subtract the decimal equivalents:** $$922 - 495 = 427$$ 4. **Convert the result back to base 4:** - Divide 427 by 4 repeatedly and record remainders: - $427 \div 4 = 106$ remainder $3$ - $106 \div 4 = 26$ remainder $2$ - $26 \div 4 = 6$ remainder $2$ - $6 \div 4 = 1$ remainder $2$ - $1 \div 4 = 0$ remainder $1$ - Reading remainders from last to first: $1 2 2 2 3$ - So, $427_{10} = 12223_4$ 5. **Final answer:** $$32122_4 - 13233_4 = 12223_4$$