2. To speed up calculations, you may want to remember these powers of 16:
160 = 1
161 = 16
162 = 256
163 = 4096
164 = 65536
1
16
= 0.0625 = 6.25 x 10-2
1
162 = 0.0039 = 3.9 x 10-3
1
163 = 0.000244 = 2.44 x 10-4
Hexadecimal Numbers – Power Tip
Mukesh N. Tekwani
3. Hexadecimal Number to Decimal Number Conversion – Example 1
Convert the hexadecimal number (B41A)16 to its decimal equivalent.
Solution:
In this example, the LSD has the weight 160, the next digit has weight 161, and then
the MSD has the weight 163.
(B41A)16 = (B x 163) + (4 x 162) + (1 x 161) + (A x 160)
(B41A)16 = (11 x 4096) + (4 x 256) + (1 x 16) + (10 x 1)
(B41A)16 = 45056 + 1024 + 16 + 10 = (46106)10
(B41A)16 = (46106)10
Mukesh N. Tekwani
LSDMSD
Hexadecimal
Number
Decimal
Number
0, 1, 2,…9 0, 1, 2,…9
A 10
B 11
C 12
D 13
E 14
F 15
4. Convert the hexadecimal number (CAB.13)16 to its decimal equivalent.
Convert the integral part CAB to
decimal:
(CAB)16 = (C x 162) + (A x 161) + (B x 160)
(CAB)16 = (12 x 162) + (10 x 161) + (11 x 160)
(CAB)16 = (12 x 256) + (10 x 16) + (11 x 1)
(CAB)16 = (3072) + (160) + (11)
(CAB)16 = (3243)10
Convert the fractional part (0.13) to
decimal:
(0.13)16 =
1
16
+
3
162
(0.13)16 = 0.0625 + 0.01172
(0.13)16 = (0.07422)10
Hexadecimal Number to Decimal Number Conversion – Example 2
Mukesh N. Tekwani
So (CAB.13)16 = (3243.07422)10
