Binary is the foundation of all computer systems. It uses only two digits: zero and one. These correspond to the OFF and ON states of electronic switches inside computers. Understanding binary is crucial for the ACSL exam as it forms the basis for data representation and computer operations.
Binary uses place values based on powers of two. From right to left, each position represents two to the power of zero, one, two, three, and so on. For example, the binary number 1011 equals one times eight, plus zero times four, plus one times two, plus one times one, which equals eleven in decimal.
To convert decimal to binary, use repeated division by two. Take thirteen as an example. Divide thirteen by two to get six with remainder one. Divide six by two to get three with remainder zero. Continue this process until the quotient becomes zero. Reading the remainders from bottom to top gives us the binary result: 1101.
Binary addition follows simple rules. Zero plus zero equals zero. Zero plus one equals one. One plus one equals ten in binary, which means write zero and carry one. Let's add 1011 and 0110. Starting from the right, we get carries that propagate left, resulting in 10001, which is seventeen in decimal.
For ACSL success, master these binary concepts: bitwise operations, signed versus unsigned numbers, two's complement for negative numbers, and overflow detection. Practice converting between decimal and binary quickly. Memorize powers of two up to 2 to the 8th power. Understanding these fundamentals will help you excel in computer science competitions.