# Binary and Hexidecimal Numbering Systems

Video Notes

Utilize other resources as you can

Khan Academy is excellent resource

Base 10 (Decimal or normal math)

0 represents nothing

1=1

2=2

3=3

4=4

5=5

6=6

7=7

8=8

9=9

10=10

Reuses symbols after 10 #’s

Base 2 (Binary)

0 or 1 (only two digits to represent everything, uses 20,1,2,3,4,etc.) 10=2 (one 2 and 0 ones)

1010=10 (0 ones, 1 two, 0 fours and 1 eight)

11=3 (one 1 and one 2)

100=4 ( one 4, 0 twos, and 0 ones)

101=5 (one 4 and one 1)

110=6 (one 4 and one 2)

111=7(one 4, one 2 and one 1)

So on and so forth

Limon’s Style for Binary

Start with 1 2 4 8 16 32 64 128 (all for networking, or continues) 256 512 1024 See what goes into the number

When you get two numbers, add them

Continue

126=1111110 (2+4+8+16+32+64=126)

42=101010 (2+8+32=42)

122=1111010 (2+8+16+32+64=122)

36=100100 (4+32=36)

18=10010 (2+16=18)

8=1000 (8=8)

10=1010 (2+8=10)

68=1000100 (64+4=68)

127=111111 (1+2+4+8+16+32+64=127)

64=1000000 (64)

10100101101=1325

Surroz’s Method (division)

Harder and how the chart does it

Hexadecimal: Limon’s Method:

0

1

2

3

4

5

6

7

8

9

A=10

B=11

C=12

D=13

E=14

F=15

Not just use these numbers/letters (0-15) in sets of four (4) to get the numbers you want (in sets of four that go 1 2 4 8) Convert to Binary first, if you must (from decimal)

Hex is ONLY the last four numbers, 1, 2, 4, 8)

Examples:

94CD=1001.0100.1100.1101

9=1001 (8+1=9)

4=0100 (4)

C (12)=1100 (8+4=12)

D (13)=1101 (8+4+1=13)

128-(through) 1 added up=255 which is why networking only goes up to 128 (8 digits) In Binary, if the number ends with a one (1) then the decimal number is odd (1, 3, 5, 7, 9, etc.)

Binary Examples:

526=1000001110 (512+8+4+2=526)

111=1101111 (64+32+8+4+2+1=111)

97=1100001 (64+32+1=97)

88=1011000 (64+16+8=88)

255=11111111 (128+64+32+16+8+4+2+1=255)

73=1001001 (64+8+1=73)

IP addresses go up to sixteen (16) million (IP addresses are related to Subnet Masking,...

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