Binary Code Basics
Explore the fundamentals of binary code, including converting between binary and decimal, and understanding its role in computers.
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Binary Code Basics
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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?
1
2
3
4
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.
True
False
10. If a computer uses 8 bits to represent a character, what is the largest decimal number that can be represented?