Binary Code Basics

Binary Code Basics

Read each question carefully and answer to the best of your ability. Show your work where applicable.

Binary code is a numbering system that uses only two symbols: 0 and 1. It's the language that computers use to process information. Each 0 or 1 is called a 'bit'.

1. Binary code uses only two symbols:   and  .

2. Each 0 or 1 in binary code is called a  .

3. Computers use   code to understand and process information.

To convert a binary number to a decimal number, you multiply each bit by a power of 2, starting from the rightmost bit with 2^0, then 2^1, 2^2, and so on. Then you add the results.

Example: Convert 1011 (binary) to decimal.

1 * 2^3 + 0 * 2^2 + 1 * 2^1 + 1 * 2^0

8 + 0 + 2 + 1 = 11 (decimal)

4. Convert the binary number 1101 to decimal.

5. Convert the binary number 10010 to decimal.

6. What is the decimal equivalent of the binary number 11?

To convert a decimal number to a binary number, you repeatedly divide the decimal number by 2 and record the remainder. The binary number is formed by reading the remainders from bottom to top.

Example: Convert 13 (decimal) to binary.

13 ÷ 2 = 6 remainder 1

6 ÷ 2 = 3 remainder 0

3 ÷ 2 = 1 remainder 1

1 ÷ 2 = 0 remainder 1

Reading remainders from bottom to top: 1101 (binary)

7. Convert the decimal number 9 to binary.

8. Convert the decimal number 20 to binary.

9. Binary code is only used by mathematicians.

10. If a computer uses 8 bits to represent a character, what is the largest decimal number that can be represented?