Binary
Artemis 2016
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Understanding Binary and Hexadecimal: A Comprehensive Guide, Study notes of Number Theory
An in-depth exploration of binary and hexadecimal systems, including their definitions, components, conversions, and uses. Learn how binary functions as a computer language, and how hexadecimal simplifies binary representation.
Typology: Study notes
2021/2022
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Binary
Artemis 2016
What Is Binary?
Binary is a language written with a combination of ones (1) and zeros (0) that
computers use to carry out commands, inputs, or functions.
Whatever you write onto a computer, a machine inside processes the input and
converts it into binary. It's like using a translator!
Converting Binary to decimal
Using a chart like this: compared to one like this:
Everywhere there is a “0” that digit is “off”
Everywhere there is a “1” that digit is “on”
An Example
Every digit in a binary number represents a power of 2. For example if we were working
with the binary number ‘00001101” we could convert it to decimal with that chart:
Off Off Off Off 8 + 4 + Off 1 =
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 128 64 32 16 8 4 2 1 0 0 0 1 0 1 0 0 128 64 32 16 8 4 2 1 0 0 0 1 0 1 1 0 128 64 32 16 8 4 2 1 0 0 0 1 0 1 1 1 128 64 32 16 8 4 2 1
Converting 23 to binary:
● Start with all numbers “off” ● Find the biggest power of two less than 23 turn it on 23 - 16 = 7 ● Find the biggest power of two less than 7 turn it on 7 - 4 = 3 ● Find the biggest power of two less than 3 turn it on 3 - 2= ● Turn on 1
What is Hexadecimal? ❖ Similar to binary, but easier to understand. ❖ It uses sixteen different symbols, the numbers zero through nine, and the letters A through F. Each symbol represents four bits. For example: 7FFFD
How to Convert Hexadecimal into Binary
123AE:
1 2 3 A E
How to Convert Hexadecimal into Binary
123AE:
1 2 3 A E
Why Binary?
Binary itself was fun because it was quick and easy to learn.
Played Binary Bingo which was very competitive and challenging.
Most of all it was interesting!
Thank You for Listening!
5468616E6B20596F7520666F72204C697374656E696E 01010100 01101000 01100001 01101110 01101011 00100000 01011001 01101111 01110101 00100000 01100110 01101111 01110010 00100000 01001100 01101001 01110011 01110100 01100101 01101110 01101001 01101110 01100111 00100001