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Describe the process of converting the binary number '10000010' to decimal.
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Layer the binary number over the conversion chart (128, 64, 32, 16, 8, 4, 2, 1). Take the values where there's a 1, ignore zeros: 128 + 2 = 130.
What number system does binary use?
Binary System uses two different numbers - 0 and 1.
List the powers of two from 2^0 to 2^3.
2^0 = 1, 2^1 = 2, 2^2 = 4, 2^3 = 8.
What is the decimal range for 7 bits?
0 to 127.
What is the result of converting the binary number '00000010' to decimal?
Layer it over the conversion chart: 2 = 2.
Convert the binary number '11111111' to decimal.
Layer it over the conversion chart: 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255.
Why are the powers of two important in binary calculations?
Binary calculations rely on powers of two since each binary digit position represents an increasing power of two, enabling straightforward conversions between binary and decimal.
How many bits form a byte, and what is another name for it?
8 bits form a byte, which is also called an octet.
What is a bit in binary terminology?
Each 0 or 1 in a binary number is called a bit.
How does the number of bits affect the range of decimal numbers that can be converted?
With more bits, the range of representable numbers increases. For example, 2 bits can represent 0-3, 3 bits can represent 0-7, continuing exponentially with each additional bit.
How many numbers can be represented with 8 bits?
8 bits can represent numbers ranging from 0 to 255.
How do you build a conversion chart to help with binary to decimal conversions?
Create a chart by doubling the value, starting from 1 on the right and moving to the left: 1, 2, 4, 8, 16, 32, 64, 128, etc.
Explain the purpose of a conversion chart in binary to decimal conversion.
A conversion chart helps in mapping binary digits to their decimal equivalents by doubling values from right to left (e.g., 1, 2, 4, 8, 16, 32, 64, 128), making it easier to convert binary numbers to decimals.
Describe a method to convert binary numbers larger than 255 to decimal.
Extend the conversion chart beyond 128 to larger values such as 256, 512, etc., following the same method of doubling each position's value.
Explain the steps to convert the decimal number '154' to binary.
1. Start with the highest chart value (128). 2. Determine if 128 fits into 154, it does: write 1. 3. Subtract 128 from 154 (26 remains). 4. Next highest value (64) does not fit into 26: write 0. 5. Continue this for all values, writing 1 only if the value fits into the remainder: Result is 10011010.
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