Question

In the following problems, you are asked to convert from one number base to another. I am aware that there are calculators that will do this for you. Thus, you must show all your work to get credit for a) Convert 101101 (base 2) to decimal (base 10). b) Convert 56 (base 8) to binary (base 2). c) Convert F2A (base 16) to binary (base 2). d) Convert 11001 (base 2) to octal (base 8).

Answer 1

a) To convert 101101 (base 2) to decimal (base 10), we can use the place value method.

Starting from the rightmost digit, we assign each digit a place value based on its position.

101101 (base 2) = 1 * 2^5 + 0 * 2^4 + 1 * 2^3 + 1 * 2^2 + 0 * 2^1 + 1 * 2^0

Simplifying this equation, we get:

101101 (base 2) = 32 + 0 + 8 + 4 + 0 + 1 = 45 (base 10)

Therefore, 101101 (base 2) is equal to 45 (base 10).

b) To convert 56 (base 8) to binary (base 2), we can use the place value method again.

Starting from the leftmost digit, we convert each digit of the base 8 number to its binary equivalent.

5 (base 8) = 101 (base 2)
6 (base 8) = 110 (base 2)

Therefore, 56 (base 8) is equal to 101110 (base 2).

c) To convert F2A (base 16) to binary (base 2), we can convert each digit of the base 16 number to its binary equivalent.

F (base 16) = 1111 (base 2)
2 (base 16) = 0010 (base 2)
A (base 16) = 1010 (base 2)

Therefore, F2A (base 16) is equal to 111100101010 (base 2).

d) To convert 11001 (base 2) to octal (base 8), we can group the binary digits into groups of three from right to left.

11 001 (base 2) = 3 1 (base 8)

Therefore, 11001 (base 2) is equal to 31 (base 8).