Example
1.8-Hex
H
Binary-
Decimal
l))o.croi
OQIJi'laiOR1
of
hexadac
il
t"'d
l digt 1 10
,,
7
He
xadecimal
1
A B 7
Con>Jert
between
he
x {
and
binary
Bits
0
10
101
1
110
11 10
11
01
1
11
o I 1 I 1 11
Convert between
he
x
and
dec
inal
{
Base
16
scale
16
3
16' 16'
16
°
Cl<:l
ci
mal
values
4096
25
6
16
,
Add
val
ues
(1
X 4096) + (10 X
256)
+ (11x 1
6)+
(7 X 1)
D
eci
m
al
l
otal
6839,o
In
Example
1.
9.
we sha,v how to co•wert
from
he
xadecimal to decimal
using
positional notation. The
conversion is 1 A87
,e
= 6839,
0
•
Example
1.9-
Hexadecimal - Decimal (posltional notation)
decimal=
(D,....,x
16°-
1
)
+ (D
0
_
2
x
1
6"-
2
)
+
···
+
(0
1
X 1
6)
+ (D
0
x
16°)
decimal= (0
3
x
16
3
)
+ (0
2
x
16
2
)
+
(O
,x
16
1
)
+
(0
0
x 16°)
decimal
= (1 x
16
3
)
+(
Ax 16
2
)
+(
Bx
16
1
)
+
(7
x 16°)
decimal=
(1 x 4096) + (10 x 256) + (
11
x 16) + (7 x 1)
decimal= (409
6)
+
(2560)
+
(176)
+ (7)
decimC1I
= 6839
In
Example
1.10,
we
show how
10
oonve
~ from
deci
mal
10
hexadecimal
using
divi
sion.
Th
e
co'11.,ers
ion is
8039,c =
01
F67
,.
. TI
,e
process is ex~clly
111,,
same
as
in Example
1.
5, excepl we divide by 16.
Example
1.10-
Dec
imal~
Hexadecimal
Division Quotient Remainder
8,039
/1
6
502
7
LS8
502 / 16 31
6
31 /
16 1
;5
F
I /
16
0 I i
....
MSB
hexmie
cim
«t =
OI
F
67
In Example 1.11,
we
show hexadecimal addition
using
t
he
following formula. which
ap
plies to any
base.
i
fx,
+ y,
2:
base(b), th
en
z, = (z1
M0Db)
an
d carry 1
The addition is
482
16
,
6A4
16
=
856
,
..
\Ive
ha,,e
deno
1e
d x
1
.y
1
,
and
z;
In
lhe
left
colu
mn
.
14
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