Chabot College
ELEC 74A
Hexadecimal Introduction
CISCO NETWORKING ACADEMY
Hexadecimal Numbers
In the decimal (base 10) system,
each digit has 10 possible values.
In the hexadecimal (base 16) system,
each digit has 16 possible values:
Dec 0
Hex 0
1
1
2
2
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3
3
4
4
5
5
6
6
7
7
8
8
9
9
10 11 12 13 14 15
A B C D E F
Hexadecimal Numbering
In decimal, each place value is a
power of ten.
103
102
101
100
1000
100
10
1
2
3
4
2
We read the number 2342 as twothousand three-hundred forty-two.
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Hexadecimal Numbering
In hexadecimal, each place value is a power of
16!
163
162
161
160
4096
256
16
1
2
3
4
2
We read the hex number 2342 as
(2 x 4096) + (3 x 256) + (4 x 16) + (2 x 1) = 9026
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Hexadecimal Notation
Is 2342 a decimal or hex number?
Hex numbers often
• are preceded by 0x:
0x2342
• are followed by h:
2342h
• include digits A - F:
2B4C
• used for MAC addresses:
00-0A-3C-24-A2-99
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Conversions
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Hexadecimal Numbering
In hex, each place value is a power of 16:
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163
162
161
160
4096
256
16
1
Hex to Decimal Conversion
The hex number 2B1F is equivalent to
11,071 in decimal:
163
162
161
160
4096
256
16
1
2
B
3
F
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2 x 4096 = 8,192
B (11) x 256 = 2,816
3 x 16 = 48
F (15) x 1 = 15
Total = 11,071
Hex to Decimal Conversion
Convert the hex number 04A3 to decimal:
163
162
161
160
4096
256
16
1
0
4
A
3
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__ x 4096 = _____
__ x 256 = _____
__ x 16 = _____
__ x 1 = _____
Total = _____
Hex to Decimal Conversion
Convert the hex number 04A3 to decimal:
163
162
161
160
4096
256
16
1
0
4
A
3
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0 x 4096 =
0
4 x 256 = 1024
A (10) x 16 = 160
3x1= 3
Total = 1187
Decimal to Hex Conversion
The decimal number 1,442 is equivalent to
5A2 in hexadecimal:
163
162
161
160
4096
256
16
1
Convert 1,442:
5
A
1442 / 256 = 5 with remainder of 162
162 / 16 = 10 (A) with remainder of 2
2/1=2
Hex Answer: 5A2
2
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Decimal to Hex Conversion
Convert the decimal number 965 to
hexadecimal:
163
162
161
160
4096
256
16
1
Convert 965:
___ / 256 = ___ with remainder of ___
___ / 16 = ___ with remainder of ___
___ / 1 = 2
Hex Answer: _____
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Decimal to Hex Conversion
Convert the decimal number 965 to
hexadecimal:
163
162
161
160
4096
256
16
1
3
C
5
Convert 965:
965 / 256 = 3 with remainder of 197
197 / 16 = 12 (C) with remainder of 5
5/1=5
Hex Answer: 3C5
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Binary Review
In binary, each place value is a power of two.
23
22
21
20
8
4
2
1
1
0
0
1
Binary 1001 is equivalent to 9 in decimal.
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Hex to Binary Conversion
• 16 = 24, so four binary bits can be
represented as a single hex digit:
Binary
1111 1110 1101 1100 1011 1010 1001 1000 0111 0110 0101 0100 0011 0010 0001 0000
Hex
F
E
D
C
B
A
9
8
7
6
5
4
3
2
1
0
Dec
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
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Hex - Binary Relationship
< 24 bits (OUI) > < 24 bits (station) >
0A-3C-19
0
A
0000 1010
3
C
0011 1100
1
9
0001 1001
24-C6-78
2
4
0010 0100
C
6
1100 0110
7
8
0111 1000
4 bits per hex digit
8 bits (one byte) per pair of hex digits
6 pairs of hex digits X 8 bits per pair = 48 bit MAC address
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Hex to Binary Conversion
• Conversions are usually done one
byte (8 bits) at a time.
• Each byte is split into two 4-bit parts.
• Each 4-bit part converts to one hex
(24) digit:
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Hex to Binary Conversion
Convert Hex C4 to Binary:
• C = 1100
• 4 = 0100
• C4 = 11000100
Binary
1111 1110 1101 1100 1011 1010 1001 1000 0111 0110 0101 0100 0011 0010 0001 0000
Hex
F
E
D
C
B
A
9
8
7
6
5
4
3
2
1
0
Dec
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
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Hex to Binary Conversion
Convert Hex 7F to Binary:
• 7 = ____
• F = ____
• 7F = ________
Binary
1111 1110 1101 1100 1011 1010 1001 1000 0111 0110 0101 0100 0011 0010 0001 0000
Hex
F
E
D
C
B
A
9
8
7
6
5
4
3
2
1
0
Dec
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
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Hex to Binary Conversion
Convert Hex 7F to Binary:
• 7 = 0111
• F = 1111
• 7F = 01111111
Binary
1111 1110 1101 1100 1011 1010 1001 1000 0111 0110 0101 0100 0011 0010 0001 0000
Hex
F
E
D
C
B
A
9
8
7
6
5
4
3
2
1
0
Dec
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
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Binary to Hex Conversion
Convert Binary 11000011 to Hex:
• 1100 = _
• 0011 = _
• 11000011 = __
Binary
1111 1110 1101 1100 1011 1010 1001 1000 0111 0110 0101 0100 0011 0010 0001 0000
Hex
F
E
D
C
B
A
9
8
7
6
5
4
3
2
1
0
Dec
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
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Binary to Hex Conversion
Convert Binary 11000011 to Hex:
• 1100 = C
• 0011 = 3
• 11000011 = C3
Binary
1111 1110 1101 1100 1011 1010 1001 1000 0111 0110 0101 0100 0011 0010 0001 0000
Hex
F
E
D
C
B
A
9
8
7
6
5
4
3
2
1
0
Dec
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
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Practice Slide
Decimal < - > Hex
163
162
161
160
4096
256
16
1
Binary < - > Hex
Binary
1111 1110 1101 1100 1011 1010 1001 1000 0111 0110 0101 0100 0011 0010 0001 0000
Hex
F
E
D
C
B
A
9
8
7
6
5
4
3
2
1
0
Dec
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
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