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### Course: AP®︎/College Computer Science Principles>Unit 1

Lesson 2: Binary numbers

# The binary number system

Binary numbers form the basis of computing systems. Binary numbers contain only the digits 0 or 1, or bits, where each bit represents a power of two. To convert binary to decimal, multiply each bit by its corresponding power of two and add the results.

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Created by Pamela Fox.

## Want to join the conversation?

• "It took us 8 bits to represent a number that only took 2 digits to represent in the decimal system."

01010101 Uses 8 bits, but I can make it with 7: 1010101.

So if we can add 0's in the front, then can't I just say,
"It took us 8 bits to represent a number [01010101] that takes a whole 10 digits to represent [0000000085] in the decimal system."

It would be nice if the video at least pointed out that you could do it in 7... anyone with me?
• From the author:That's a really good point. YouTube doesn't make it particularly easy to edit videos, but I'll try to edit it if I get the chance. I very much agree.
• How many bytes does it take to equal one KB
(1 vote)
• 1024 bytes
• *Humming intesifies
• Why do they leave the 0 there, typically its not supposed to do that, like I wouldn't say 010, I would just say 10.
• Binary numbers are generally only used in the context of computers which use a fixed number of bytes/bits to represent numbers. For example, a computer may use 32 bits to represent the number 13 even though 13 would only need 4 bits. This leaves 28 preceding 0s in the binary representation of 13. So, in general, we are less concerned about getting rid of preceding 0s when we write out binary numbers.
• how do you figure out how many bytes does it take to equal one KB?
• Does anyone know the reason why that it's easier for computers to calculate in binary system but not the decimal?
• A string of binary represents electrical flow through the circuit (which can only be easy detected with an 0/1 signal). This cannot be done through decimal numbers.
• 001000111100111😑. Guess what it is!
• 53426
= 2^15 + 2^14 + 2^12 + 2^7 + 2^5 + 2^4 + 2^1
= 1*2^15 + 1*2^14 + 0*2^13 + 1*2^12 + 0*2^11 + 0*2^10 + 0*2^9 +
0*2^8 + 1*2^7 + 0*2^6 + 1*2^5 + 1*2^4 + 0*2^3 + 0*2^2 +
1*2^1 + 0*2^0
= 1101000010110010 i do not no what this means It took us 8 bits to represent a number that only took 2 digits to represent in the decimal system."

01010101 Uses 8 bits, but I can make it with 7: 1010101.

So if we can add 0's in the front, then can't I just say,
"It took us 8 bits to represent a number [01010101] that takes a whole 10 digits to represent [0000000085] in the decimal system."

It would be nice if the video at least pointed out that you could do it in 7... anyone with me?