Binary Code Basics
A worksheet to introduce 7th-grade students to the fundamentals of binary code, including converting between binary and decimal numbers.
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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 for conversion problems.
Binary code is a fundamental concept in computing. It's a number system that uses only two symbols: 0 and 1. These are called bits. Our everyday number system, the decimal system, uses ten symbols (0-9). Understanding binary helps us understand how computers process information.
1. How many symbols does the binary number system use?
One
Two
Ten
Twenty
2. What is the smallest unit of information in binary code called?
Byte
Nibble
Bit
Word
3. The binary system is a base- number system.
4. The decimal system is a base- number system.
To convert a binary number to a decimal number, you multiply each bit by powers of 2, starting from the rightmost bit as 2^0, then 2^1, 2^2, and so on. Then you add the results.
Example: Convert 1011 (binary) to decimal.
1 x 2^3 + 0 x 2^2 + 1 x 2^1 + 1 x 2^0
= 1 x 8 + 0 x 4 + 1 x 2 + 1 x 1
= 8 + 0 + 2 + 1 = 11 (decimal)
5. Convert the binary number 1101 to its decimal equivalent.
6. Convert the binary number 10010 to its decimal equivalent.
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
Read remainders bottom-up: 1101 (binary)
7. Convert the decimal number 9 to its binary equivalent.
8. Convert the decimal number 25 to its binary equivalent.
9. Computers primarily use the decimal number system to process information.
True
False
10. The binary number 10 is equivalent to the decimal number 2.
True
False