Solve the problem, 11101/111 in binary using long division.
To solve the problem using long division, we need to convert the numbers into binary representation:
11101 in binary is 101101011
111 in binary is 1101111
Now, let's perform long division:
_________
1101111 | 101101011
- 1101111
__________
111000
- 1101111
___________
100011
- 1101111
____________
As we can see, the remainder (100011) cannot be divided further and is less than the divisor (1101111). Therefore, our final result is:
11101 / 111 in binary is 100011
To solve the problem, 11101/111 in binary using long division, follow these steps:
Step 1: Set up the division problem:
______________
111 | 11101
-
Step 2: Start from the leftmost digit of the dividend (11101), and divide it by the divisor (111).
Step 3: Since the divisor (111) is larger than the leftmost digits (11101), bring down the next digit from the dividend.
Step 4: Now, divide the new number (111011) by the divisor (111).
Step 5: The result of this division is 1001, so write it above the line.
1001
______________
111 | 11101
-
Step 6: Multiply the divisor (111) by the quotient (1001) and write the product below the dividing line, aligning the numbers correctly.
1001
______________
111 | 11101
111
-
Step 7: Subtract the product (111) from the current partial dividend (11101) and write the remainder below the line.
1001
______________
111 | 11101
111
-
10
Step 8: Since we have a remainder (10), bring down the next digit from the dividend.
1001
______________
111 | 11101
111
-
10
-
Step 9: Divide the new number (101) by the divisor (111).
Step 10: The result of this division is 1, so write it above the line.
1001
______________
111 | 11101
111
-
101
-
Step 11: Multiply the divisor (111) by the new quotient (1) and write the product below the dividing line.
1001
______________
111 | 11101
111
-
101
111
-
Step 12: Subtract the product (111) from the current partial dividend (101) and write the remainder below the line.
1001
______________
111 | 11101
111
-
101
111
-
10
Step 13: We have a remainder (10). Bring down the next digit from the dividend.
1001
______________
111 | 11101
111
-
101
111
-
10
-
Step 14: Divide the new number (100) by the divisor (111).
Step 15: The result of this division is 0, so write it above the line.
1001
______________
111 | 11101
111
-
101
111
-
10
-
0
Step 16: Multiply the divisor (111) by the new quotient (0) and write the product below the dividing line.
1001
______________
111 | 11101
111
-
101
111
-
10
-
0
-
Step 17: Subtract the product (0) from the current partial dividend (100) and write the remainder below the line.
1001
______________
111 | 11101
111
-
101
111
-
10
-
0
-
100
Step 18: There are no more digits remaining in the dividend. We have the final remainder (100).
Step 19: The quotient is the combined quotients from all the divisions (1001, 1, 0) in reverse order, resulting in 101100.
Therefore, the solution to 11101/111 in binary using long division is:
quotient = 101100
remainder = 100
To solve the problem 11101/111 in binary using long division, follow these steps:
Step 1: Set up the division
- Write the dividend (11101) and the divisor (111) on top of each other, aligning the binary digits.
- Set up the division by placing a bar between the dividend and divisor.
______
11101 | 111
Step 2: Find the first quotient digit
- Look at the leftmost digit of the dividend (1) and see if it's greater than or equal to the divisor (111). In this case, it is.
- Write the quotient digit (1) above the bar, aligned with the leftmost digit of the dividend.
- Multiply the divisor (111) by the quotient digit (1) and write the result (111) below the dividend.
______
11101 | 111
1
111
Step 3: Subtract and bring down the next digit
- Subtract the result (111) from the first part of the dividend (11101 - 111 = 11010).
- Bring down the next digit of the dividend.
______
11101 | 111
1
111
-----
11010
Step 4: Find the next quotient digit
- Look at the leftmost digit of the new dividend (11010) and see if it's greater than or equal to the divisor (111). In this case, it is.
- Write the quotient digit (1) above the bar, aligned with the new leftmost digit of the dividend.
- Multiply the divisor (111) by the quotient digit (1) and write the result (111) below the new dividend.
______
11101 | 111
11
111
-----
11010
111
---
110
Step 5: Subtract and bring down the next digit
- Subtract the result (111) from the second part of the dividend (11010 - 111 = 10111).
- Bring down the next digit of the dividend.
______
11101 | 111
11
111
-----
11010
111
---
110
1
Step 6: Find the next quotient digit
- Look at the leftmost digit of the new dividend (1101) and see if it's greater than or equal to the divisor (111). In this case, it is.
- Write the quotient digit (1) above the bar, aligned with the new leftmost digit of the dividend.
- Multiply the divisor (111) by the quotient digit (1) and write the result (111) below the new dividend.
______
11101 | 111
111
111
-----
11010
111
---
110
1
111
Step 7: Subtract and bring down the next digit
- Subtract the result (111) from the third part of the dividend (1101 - 111 = 100).
- Bring down the next digit of the dividend.
______
11101 | 111
111
111
-----
11010
111
---
110
1
111
100
Step 8: Find the last quotient digit
- Look at the leftmost digit of the new dividend (100) and see if it's greater than or equal to the divisor (111). In this case, it is.
- Write the quotient digit (1) above the bar, aligned with the new leftmost digit of the dividend.
- Multiply the divisor (111) by the quotient digit (1) and write the result (111) below the new dividend.
______
11101 | 111
111
111
-----
11010
111
---
110
1
111
100
111
Step 9: Subtract and bring down the next digit
- Subtract the result (111) from the fourth part of the dividend (100 - 111 = -11).
- Since the result is negative and there are no more digits to bring down, the division is complete.
Step 10: Interpret the quotient
- The quotient is obtained by reading the quotient digits from top to bottom (1, 1, 1, 0, 1).
Therefore, 11101/111 in binary is equal to 11101 divided by 111, which gives a quotient of 11101.