Find the value of 1011011 base 2 ÷ 111 base 2
To divide two numbers in binary, set up the division problem similar to how you would in decimal and perform repeated subtraction or long division.
The dividend is 1011011 base 2 (which is 91 in decimal), and the divisor is 111 base 2 (which is 7 in decimal).
100011 (quotient) <- Start with a 0 in the quotient
_______________
111 | 1011011 (dividend)
- 111
___________
100111
- 111
_______
1110
- 111
______
1111
- 111
_______
0
The remainder is 0, indicating that the division process is complete. The quotient is 100011 base 2.
To divide two numbers in binary format, we can use long division. Let's divide 1011011 base 2 by 111 base 2 step-by-step.
Step 1: Write the dividend (1011011 base 2) and the divisor (111 base 2) in long division format:
_______
111 | 1011011
Step 2: Determine the first quotient digit by calculating how many times the divisor can be subtracted from the leftmost digits of the dividend without exceeding it.
In this case, we can subtract 111 from 1011 (the leftmost 4 digits of the dividend) once:
_______
111 | 1011011
- 111
_______
1000
Step 3: Bring down the next digit from the dividend.
In this case, we bring down the next digit, which is 1:
_______
111 | 1011011
- 111
_______
1000
1
Step 4: Repeat steps 2 and 3 until you have no more digits in the dividend.
In this case, we can subtract 111 from 1000 (the current dividend) once:
_______
111 | 1011011
- 111
_______
1000
1
- 111
_______
100
Since we have no more digits in the dividend, we stop here.
Step 5: The quotient is the series of quotient digits we obtained in step 2.
In this case, the quotient is 10.
Therefore, the value of 1011011 base 2 ÷ 111 base 2 is 10.
To find the value of 1011011 base 2 divided by 111 base 2, we need to perform binary division. Here's how you can do it step by step:
Step 1: Set up the division problem
Write the dividend (1011011 base 2) inside the long division bracket and the divisor (111 base 2) on the left side of the bracket.
1011011 ÷ 111
Step 2: Start the division
Look at the leftmost digit of the dividend and determine if it is divisible by the divisor. If it is, write the quotient above the long division bracket. Otherwise, bring down the next digit and combine it with the previous digit to form a new number to divide.
1011011 ÷ 111
1
Step 3: Perform the division
Multiply the divisor by the quotient and write the result below the dividend. Then subtract the result from the dividend to get the remainder.
111
________
111
---------
100
________
Step 4: Bring down the next digit
Bring down the next digit of the dividend (in this case, the digit is 0) to the right of the remainder.
111
________
111
---------
1000
Step 5: Perform the division again
Repeat the steps of multiplication and subtraction until you have no more digits in the dividend.
111
________
111
---------
1000
111
---------
10010
111
---------
111
______
00
Step 6: Write the final answer
The division is complete when there are no more digits in the dividend. The quotient is the final answer.
Therefore, 1011011 base 2 ÷ 111 base 2 equals 10010 remainder 00.
In decimal notation, the answer would be 18 with a remainder of 0.