ALU 101 Binary Number Systems

Question 1

What is the decimal equivalent of the binary number 1011?

Accepted Answer

11

Answer

1011 in binary = 1×8 + 0×4 + 1×2 + 1×1 = 8 + 0 + 2 + 1 = 11 in decimal.

Question 2

How many bits are required to represent the decimal number 255?

Accepted Answer

8

Answer

255 = 2⁸ − 1, so 8 bits are needed to represent it (11111111 in binary).

Question 3

What is the hexadecimal representation of the binary number 11001010?

Accepted Answer

CA

Answer

Splitting 11001010 into nibbles gives 1100 (C) and 1010 (A), so the hex value is CA.

Question 4

In the two's complement system, what is the two's complement of 0101 (4-bit)?

Accepted Answer

1011

Answer

Invert 0101 to get 1010, then add 1 to get 1011, which is the two's complement of 0101.

Question 5

Which number base is most commonly used internally by ALU hardware?

Accepted Answer

Binary (base 2)

Answer

ALUs operate internally on binary (base 2) data because digital circuits use two voltage states representing 0 and 1.

ALU 101 - Arithmetic Logic Unit 101 Exam Practice Test