Question

Transform the decimal number 43 into a binary system, and then transform the binary number 110011001 into a decimal system.

Answer 1

To convert decimal to binary, repeatedly divide by 2 and record the remainders. To convert binary to decimal, assign exponents of 2 to each digit and calculate the sum.

Step-by-step explanation:

To convert the decimal number 43 into binary, we can use the process of repeated division by 2. Dividing 43 by 2 gives us a quotient of 21 and a remainder of 1. Dividing the quotient (21) by 2 gives us a new quotient of 10 and a remainder of 1. Dividing the new quotient (10) by 2 gives us a quotient of 5 and a remainder of 0. Finally, dividing the remaining quotient (5) by 2 gives us a quotient of 2 and a remainder of 1. The binary representation of 43 is 101011.

To convert the binary number 110011001 into decimal, we need to determine the place value of each digit. Starting from the rightmost digit, we assign exponents of 2 to each digit, starting from 0. Using this method, the decimal representation of 110011001 is 409 + 256 + 9 = 674.