Binary and Hexidecimal Numbering Systems
Binary and Hexadecimal 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,
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,