Hexadecimal Number System

What is Hexadecimal Number System?

  • Hexadecimal System employs 16 as a base, requiring 16 distinct symbols 0 to 9 and A to F for its digits.
  • Also known as base 16 numbers. The digits have a value specified which is equal to the base number ( 16 ) 0,1,2,3,4,5,6,7......n from right to left.
Hexadecimal: 0 1 2 3 4 5 6 7 8 9 A B C D E F
Decimal: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

How to convert Hexadecimal to Binary?

  • Each hexadecimal digit represents 4 binary digits (bits).
  • convert each digit of the hexadecimal number to binary using the below table.
Hexadecimal: 0 1 2 3 4 5 6 7 8 9 A B C D E F
Binary: 0 1 10 11 100 101 110 111 1000 1001 1010 1011 1100 1101 1110 1111

Example:

  • 1E3 = 0001 1110 0011
  • 1F2 = 0001 1111 0010
  • 1C1 = 0001 1100 0001

How to convert Hexadecimal to Decimal?

  • Multiply each digit of the given number with the specified value.
  • The specified value is 16index . The index starts from 0 and is incremented by 1 from right to left.
  • Add the results.

Example:


Hex
base 16
Decimal
base 10
Calculation
0 0 -
1 1 -
2 2 -
3 3 -
4 4 -
5 5 -
6 6 -
7 7 -
8 8 -
9 9 -
A 10 -
B 11 -
C 12 -
D 13 -
E 14 -
F 15 -
10 16 1×161+0×160 = 16
11 17 1×161+1×160 = 17
12 18 1×161+2×160 = 18
13 19 1×161+3×160 = 19
14 20 1×161+4×160 = 20
15 21 1×161+5×160 = 21
16 22 1×161+6×160 = 22
17 23 1×161+7×160 = 23
18 24 1×161+8×160 = 24
19 25 1×161+9×160 = 25
1A 26 1×161+10×160 = 26
1B 27 1×161+11×160 = 27
1C 28 1×161+12×160 = 28
1D 29 1×161+13×160 = 29
1E 30 1×161+14×160 = 30
1F 31 1×161+15×160 = 31
20 32 2×161+0×160 = 32
30 48 3×161+0×160 = 48
40 64 4×161+0×160 = 64
50 80 5×161+0×160 = 80
60 96 6×161+0×160 = 96
70 112 7×161+0×160 = 112
80 128 8×161+0×160 = 128
90 144 9×161+0×160 = 144
A0 160 10×161+0×160 = 160
B0 176 11×161+0×160 = 176
C0 192 12×161+0×160 = 192
D0 208 13×161+0×160 = 208
E0 224 14×161+0×160 = 224
F0 240 15×161+0×160 = 240
100 256 1×162+0×161+0×160 = 256
200 512 2×162+0×161+0×160 = 512
300 768 3×162+0×161+0×160 = 768
400 1024 4×162+0×161+0×160 = 1024

Uses and advantanges:

  • Used by computer system designers and programmers.
  • Each hexadecimal digit represents 4 binary digits.
  • Hex numbers can be easily converted to binary.
  • This format is quite compact and much easier to understand.
  • Byte in binary can range from 00000000 to 11111111 which can be made more convinient represented as 00 to FF in hex.
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