1. **State the problem:** We need to find how many units (1s) are in the binary representation of the value of the expression $42014 + 22015 - 8$. 2. **Calculate the value of the expression:** $$42014 + 22015 - 8 = 42014 + 22015 - 8$$ $$= 64029 - 8 = 64021$$ 3. **Convert the decimal number 64021 to binary:** We repeatedly divide by 2 and record the remainders: - $64021 \div 2 = 32010$ remainder $1$ - $32010 \div 2 = 16005$ remainder $0$ - $16005 \div 2 = 8002$ remainder $1$ - $8002 \div 2 = 4001$ remainder $0$ - $4001 \div 2 = 2000$ remainder $1$ - $2000 \div 2 = 1000$ remainder $0$ - $1000 \div 2 = 500$ remainder $0$ - $500 \div 2 = 250$ remainder $0$ - $250 \div 2 = 125$ remainder $0$ - $125 \div 2 = 62$ remainder $1$ - $62 \div 2 = 31$ remainder $0$ - $31 \div 2 = 15$ remainder $1$ - $15 \div 2 = 7$ remainder $1$ - $7 \div 2 = 3$ remainder $1$ - $3 \div 2 = 1$ remainder $1$ - $1 \div 2 = 0$ remainder $1$ Reading remainders from bottom to top, the binary representation is: $$1111101100010101_2$$ 4. **Count the number of 1s in the binary representation:** The binary number $1111101100010101$ has the following digits: - $1,1,1,1,1,0,1,1,0,0,0,1,0,1,0,1$ Counting the 1s: There are $10$ ones. **Final answer:** The binary representation of $42014 + 22015 - 8$ contains $10$ units (1s).