## GCSE Computer Science: Binary System

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### Frequently Asked Questions

#### What is the binary system used for in computer science?

The binary system is used to represent digital data in computer systems. Since computers work with electronic signals that can only have two states (on or off), the binary system allows them to store, process, and communicate information in a way that is easily interpreted by electronic circuits.

#### How do you convert a binary number to a decimal number?

To convert a binary number to a decimal number, you need to add up the values of each digit in the binary number, starting from the rightmost digit. Each digit in a binary number represents a power of 2, so you multiply the digit by its corresponding power of 2 and add up the results. For example, the binary number 1010 is equivalent to the decimal number 10: (1 x 2^3) + (0 x 2^2) + (1 x 2^1) + (0 x 2^0) = 8 + 0 + 2 + 0 = 10.

#### What is the largest decimal number that can be represented using 8 bits in binary?

Using 8 bits, the largest decimal number that can be represented in binary is 255. This is because 8 bits can represent 2^8 = 256 different values, ranging from 0 to 255.

#### How do you perform binary addition?

To perform binary addition, you start by adding the rightmost digits together. If the sum of the two digits is less than 2, you write that sum in the result. If the sum is equal to or greater than 2, you write the remainder (which is either 0 or 1) in the result and carry over a 1 to the next column. You then repeat this process for the next column to the left, adding any carried-over digits from the previous column.

#### How do you perform binary subtraction?

To perform binary subtraction, you use the same method as binary addition, but with some differences. Instead of adding the digits, you subtract the rightmost digit of the second number from the rightmost digit of the first number. If the first number is smaller than the second number, you borrow a 1 from the next column to the left. You then repeat this process for the rest of the digits, subtracting any borrowed digits from the next column.