Hexadecimal Numbers - Quiz Explanation

The correct answers are indicated below, along with the text that explains the correct answers.

1.	Which of the following is not a valid hexadecimal digit? Please select the best answer.
	A.	0
	B.	G
	C.	F
	The correct answer is B. Each digit in a hexadecimal number can be one of the numerals 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9, or one of the letters A, B, C, D, E, or F. Thus G is not a valid hexadecimal digit.

2.	What is the binary representation of the hexadecimal number `AC3F`? Please select the best answer.
	A.	`1010110000111111`
	B.	`1100101011110011`
	C.	`1111001111001010`
	The correct answer is A. Replacing each hexadecimal digit with the corresponding 4-bit binary number, we see that `AC3F` is equivalent to the binary number `1010110000111111`. In other words, the hexadecimal digits A, C, 3, and F are equivalent to the 4-bit binary numbers `1010`, `1100`, `0011`, and `1111` respectively.

3.	What is the hexadecimal representation of the binary number `01111110`? Please select the best answer.
	A.	E7
	B.	3D
	C.	7E
	The correct answer is C. Replacing each group of 4 binary digits with the corresponding hexadecimal digit, we see that `01111110` is equivalent to the hexadecimal number 7E. In other words, the hexadecimal digit for `0111` is 7 and the hexadecimal digit for `1110` is E.