Divide 10001111 by 1011 and compare the result as obtained in decimal system
The Correct Answer and Explanation is:
Let’s divide the binary numbers 10001111 by 1011 and compare the result with the decimal system.
Step 1: Convert Binary Numbers to Decimal
- The binary number 10001111 can be converted to decimal as follows: 100011112=(1×27)+(0×26)+(0×25)+(0×24)+(1×23)+(1×22)+(1×21)+(1×20)10001111_2 = (1 \times 2^7) + (0 \times 2^6) + (0 \times 2^5) + (0 \times 2^4) + (1 \times 2^3) + (1 \times 2^2) + (1 \times 2^1) + (1 \times 2^0)100011112=(1×27)+(0×26)+(0×25)+(0×24)+(1×23)+(1×22)+(1×21)+(1×20) 100011112=128+8+4+2+1=1431010001111_2 = 128 + 8 + 4 + 2 + 1 = 143_{10}100011112=128+8+4+2+1=14310
- The binary number 1011 can be converted to decimal as follows: 10112=(1×23)+(0×22)+(1×21)+(1×20)1011_2 = (1 \times 2^3) + (0 \times 2^2) + (1 \times 2^1) + (1 \times 2^0)10112=(1×23)+(0×22)+(1×21)+(1×20) 10112=8+2+1=11101011_2 = 8 + 2 + 1 = 11_{10}10112=8+2+1=1110
Step 2: Perform the Division in Decimal
Now, divide the decimal equivalents: 14311=13\frac{143}{11} = 1311143=13
Step 3: Convert the Result Back to Binary
The quotient is 13 in decimal. We can convert 13 to binary: 1310=(1×23)+(0×22)+(0×21)+(1×20)=1101213_{10} = (1 \times 2^3) + (0 \times 2^2) + (0 \times 2^1) + (1 \times 2^0) = 1101_21310=(1×23)+(0×22)+(0×21)+(1×20)=11012
Conclusion
- Binary Division: 10001111 ÷ 1011 results in 1101 in binary.
- Decimal Division: The result of dividing 143 by 11 gives 13 in decimal, which confirms that the binary result 1101 corresponds to the decimal result 13.
Both methods give the same result, and the comparison shows that the binary division accurately represents the decimal operation. The key takeaway is the consistency between the two systems, with binary numbers directly corresponding to their decimal equivalents.
