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A short class with Sarah and her students. The other ways are under More.
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Today, we are diving into the Binary Number System, which is essential for understanding how computers work. Can anyone tell me what a binary number looks like?
Isn't it just 0s and 1s?
Exactly! The Binary Number System uses just two symbols: 0 and 1. We call each digit a 'bit.' Why do you think computers use binary?
Because they have circuits that can only be either on or off?
Great observation! The internal circuitry uses these two states to perform operations. Let's remember that: 'Binary = Two States!'
Now, moving on to conversions. How do we convert a binary number, say 1101, into decimal?
Uh, do we multiply each digit by powers of 2?
Correct! For 1101, we expand it like this: 1×2^3 + 1×2^2 + 0×2^1 + 1×2^0. Can anyone work out that calculation?
That would be 8 + 4 + 0 + 1, which equals 13!
Fantastic! You just converted binary 1101 to decimal 13. Remember, practice will make you proficient!
Let's flip the process. How do we convert decimal, say 13, into binary?
I think we use successive divisions by 2?
That's right! We keep dividing 13 by 2 and noting the remainders. Let's walk through it together.
So we divide 13 by 2, and that's 6 remainder 1?
Yes! Next, divide 6 by 2. What do we get?
That’s 3 remainder 0. We keep doing this until we reach 0.
Exactly! And reading the remainders from bottom to top gives us our binary number 1101!
In Binary, it's 0s and 1s, that’s how a computer runs.
Once upon a time in a computer’s brain, it could only think in 0s and 1s, but through these, it learned to play.
To convert from Binary to Decimal, 'Bits are Powers' - remember to calculate each bit's power of 2.
BCD means 'Binary, Convert, Decimal' - a simple way to remember the conversion process.
Term
What is binary?
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Term
What does 'bit' refer to?
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The Binary Number System uses only two digits, 0 and 1, crucial for computer operations.
The Binary Number System (base-2) forms the foundation of computing, representing values with bits. It is utilized in converting numbers between binary and decimal, which is essential for various computer functions and data interpretation.
The Binary Number System is a base-2 numeral system that employs two digits, 0 and 1, making it the simplest number system used in computing. Each digit in a binary number is referred to as a 'bit.' Computers rely on binary because their internal circuitry can only represent two states: on (1) and off (0). This section discusses how to convert binary numbers to decimal and decimal numbers to binary through outlined methods. For binary to decimal conversion, one expands the binary number using powers of 2, while for decimal to binary conversion, one uses successive divisions by 2. Examples provided include converting the binary number 1101 to decimal, resulting in 13, and the decimal number 13 to binary, resulting in 1101. The knowledge of these conversions is foundational for understanding how computers process numeric data.