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## Algebra (all content)

### Course: Algebra (all content)>Unit 1

Lesson 14: Binary and hexadecimal number systems

# Converting larger number from decimal to binary

## Want to join the conversation?

• So I wonder is this is why most phones or tablets come with the the option of 16, 32, 64 etc. megabytes of memory is due to the binary system used in computing.
• I'd say you're right. Electronic memory is a collection of a large number of elements, each of which has only two states (on and off). Computers operate in binary. So, if you've got a really huge number of these binary units, the information they can hold, all of them put together, is still a power of two bits.
However, I suspect this view is a little simplistic, since some of the memory is probably reserved for things you can't ever erase on a phone or a computer. And there are probably other technicalities that complicate the matter, but basically—yes, computers using binary lead to numbers that are powers of two at the other end.
• Like the Base 10 number system, would there be an infinite amount of zeros before the start of a number that you just don't bother to write? So a binary number always starts with a 1?
• Yes, there is an infinite amount of zeros before the first one in binary, you just don't bother to write it.
• i just noticed that around , sal has left 2^2=4 in the table of powers of 2 given in the right side of this video. is that a mistake?
• how do we convert a floating point number like 1.21 into binary?
• Sir 114 is not large enough number. You should have taken something like 91232148. Now how can we decompose it into powers of 2? Of course we will not get such a big number but what if we get?
• For such a large number I assume you would need the hexadecimal system.
• i've read somewhere that bytes typically have 8 numbers in their binary code and this one only has 7. So would there be a 0 in the front?
• Yes! Zero wiil be in front if the no. of digits are deficient.
• Why did Sal skip 2 to the 2nd power? Did he forget to write that or was that on purpose?
• So how do we convert larger numbers? Isn't binary all about 0s and 1s? Or could we have a 5 in the 64s place?
• Nobody know this method?

1.Divide the number by 2
2.Record the result and the remainder
3.Continue to divide the result by 2
4.Stop until the result is 0

For instance:
19578
19578/2 =9789 remain 0
9789/2 =4894 remain 1
4894/2 =2447 remain 0
2447/2 =1223 remain 1
1223/2 =611 remain 1
611/2 =305 remain 1
305/2 =152 remain 1
152/2 =76 remain 0
76/2 =38 remain 0
38/2 =19 remain 0
19/2 =9 remain 1
9/2 =4 remain 1
4/2 =2 remain 0
2/2 =1 remain 0
1/2 =0 remain 1

Hence the binary of 19578 is
100 110 001 111 010