Find the product of 2310 and 1112 and give the answer in both base 10 and base 2.
To find the product of 2310 and 1112, we can simply multiply the two numbers together.
2310 * 1112 = 2,574,120
The product in base 10 is 2,574,120.
To convert this number to base 2, we can use the division by 2 method.
First, let's divide 2,574,120 by 2:
2,574,120 ÷ 2 = 1,287,060 with a remainder of 0
Next, let's divide 1,287,060 by 2:
1,287,060 ÷ 2 = 643,530 with a remainder of 0
We continue this process until we reach 0.
643,530 ÷ 2 = 321,765 with a remainder of 0
321,765 ÷ 2 = 160,882 with a remainder of 1
160,882 ÷ 2 = 80,441 with a remainder of 0
80,441 ÷ 2 = 40,220 with a remainder of 1
40,220 ÷ 2 = 20,110 with a remainder of 0
20,110 ÷ 2 = 10,055 with a remainder of 0
10,055 ÷ 2 = 5,027 with a remainder of 1
5,027 ÷ 2 = 2,513 with a remainder of 1
2,513 ÷ 2 = 1,256 with a remainder of 1
1,256 ÷ 2 = 628 with a remainder of 0
628 ÷ 2 = 314 with a remainder of 0
314 ÷ 2 = 157 with a remainder of 0
157 ÷ 2 = 78 with a remainder of 1
78 ÷ 2 = 39 with a remainder of 0
39 ÷ 2 = 19 with a remainder of 1
19 ÷ 2 = 9 with a remainder of 1
9 ÷ 2 = 4 with a remainder of 1
4 ÷ 2 = 2 with a remainder of 0
2 ÷ 2 = 1 with a remainder of 0
1 ÷ 2 = 0 with a remainder of 1
The remainders from bottom to top give us the base 2 representation of the product:
2,574,120 in base 2 is 1001110110100111011000
To find the product of 2310 and 1112, we can simply multiply the two numbers together.
Step 1: Multiply the ones digits: 0 * 2 = 0.
Step 2: Multiply the tens digits: 1 * 1 = 1.
Step 3: Multiply the hundreds digits: 3 * 1 + 1 * 2 = 5.
Step 4: Multiply the thousands digits: 2 * 1 + 3 * 1 = 5.
Step 5: Multiply the ten-thousands digits: 1 * 1 = 1.
So the product of 2310 and 1112 is 2571120.
To convert this into binary (base 2), we need to divide the product by 2 repeatedly, using the remainder as the binary digits.
Step 1: Divide 2571120 by 2. The quotient is 1285560 and the remainder is 0.
Step 2: Divide 1285560 by 2. The quotient is 642780 and the remainder is 0.
Step 3: Divide 642780 by 2. The quotient is 321390 and the remainder is 0.
Step 4: Divide 321390 by 2. The quotient is 160695 and the remainder is 0.
Step 5: Divide 160695 by 2. The quotient is 80347 and the remainder is 1.
Step 6: Divide 80347 by 2. The quotient is 40173 and the remainder is 1.
Step 7: Divide 40173 by 2. The quotient is 20086 and the remainder is 0.
Step 8: Divide 20086 by 2. The quotient is 10043 and the remainder is 0.
Step 9: Divide 10043 by 2. The quotient is 5021 and the remainder is 1.
Step 10: Divide 5021 by 2. The quotient is 2510 and the remainder is 1.
Step 11: Divide 2510 by 2. The quotient is 1255 and the remainder is 0.
Step 12: Divide 1255 by 2. The quotient is 627 and the remainder is 1.
Step 13: Divide 627 by 2. The quotient is 313 and the remainder is 1.
Step 14: Divide 313 by 2. The quotient is 156 and the remainder is 1.
Step 15: Divide 156 by 2. The quotient is 78 and the remainder is 0.
Step 16: Divide 78 by 2. The quotient is 39 and the remainder is 0.
Step 17: Divide 39 by 2. The quotient is 19 and the remainder is 1.
Step 18: Divide 19 by 2. The quotient is 9 and the remainder is 1.
Step 19: Divide 9 by 2. The quotient is 4 and the remainder is 1.
Step 20: Divide 4 by 2. The quotient is 2 and the remainder is 0.
Step 21: Divide 2 by 2. The quotient is 1 and the remainder is 0.
Step 22: Divide 1 by 2. The quotient is 0 and the remainder is 1.
So, converting the product 2571120 into binary (base 2), we get 1001110110100001100000.