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Base number system

This is another very important concept in computer science. Particularly because of how data is represented within machines.
Taking up bit arithmetic as a topic separately, let us initiate with understanding what those terms even mean.

In our customary base-ten system, we have digits for the numbers zero through nine. We do not have a single-digit numeral for “ten”. Yes, we write “10”, but its two digits; we have no single solitary digit that stands for “ten”.

There are 10 digits using which we represent all the numbers. Hence the base 10 system.

Similarily, binary number system or base 2 number system has only 2 digits 0, 1. Hex number system or base 16 number system has 16 digits ( 0, 1, 2 .. 9, A, B, .. F ). In general a N base number system has N digits, 0, 1, ... N-1 ( The digits usually after 9 are represented as A, B and so on ).

Base systems like binary and hexadecimal seem a bit strange at first. The key is understanding how different systems “tick over” like an odometer when they are full.

Base 10, our decimal system, “ticks over” when it gets 10 items, creating a new digit. We wait 60 seconds before “ticking over” to a new minute. Hexadecimal and binary are similar, but tick over every 16 and 2 items, respectively.

In computers, numbers are internally represented in binary number system.
We explore more in next slides.

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Math Problems

Base conversion
Problem Score Companies Time Status
Excel Column Number 175 23:19
Excel Column Title 175 41:11
Digit op
Problem Score Companies Time Status
Palindrome Integer 200
Reverse integer 200 28:36
Next Smallest Palindrome! 400 58:55
Number encoding
Problem Score Companies Time Status
Next Similar Number 200 54:52
Rearrange Array 250
Array dp
Problem Score Companies Time Status
Numbers of length N and value less than K 200
Problem Score Companies Time Status
City Tour 300
Grid Unique Paths 375 32:35
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