Erik Jonsson School of Engineering and
Th
U i
it
f T
t D ll
Computer Science
The University of Texas at Dallas
Easier Ways to Express Binary Numbers
•
Unfortunately, we were not born with 4 (or 8!) fingers per hand.
•
The reason is that it is relatively difficult to convert binary numbers
to decimal, and vice-versa.
•
However, converting hexadecimal (base-16) numbers back and forth
to binary is very easy (the octal, or base-8, number system was also
used at one time).
4
•
Since 16 = 2
, it is very easy to convert a binary number of any length
into hexadecimal form, and vice-versa:
0
16
= 0
10
=
0000
2
4
16
= 4
10
=
0100
2
8
16
=
8
10
=
1000
2
C
16
= 12
10
=
1100
2
1
1
0001
5
5
0101
9
9
1001
D
13
1101
16
= 1
10
=
2
16
= 5
10
=
2
16
=
10
=
2
16
= 13
10
=
2
2
16
= 2
10
=
0010
2
6
16
= 6
10
=
0110
2
A
16
= 10
10
=
1010
2
E
16
= 14
10
=
1110
2
3
16
= 3
10
=
0011
2
7
16
= 7
10
=
0111
2
B
16
= 11
10
=
1011
2
F
16
= 15
10
=
1111
2
•
The letters that stand for hexadecimal numbers above 9 can be upper
© N. B. Dodge 9/09
1
Lecture #2:
Signed Binary Numbers and Binary Codes
The letters that stand for hexadecimal numbers above 9 can be upper
or lower case – both are used.
Note that one nibble = one hex digit.

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Erik Jonsson School of Engineering and
Th
U i
it
f T
t D ll
Computer Science
The University of Texas at Dallas
Binary-Hexadecimal
•
Since 2
4
= 16, each hex digit effectively represents the same numeric
count as four binary digits.
A
th
t
thi i th t
l
i
h
b
i th
•
Another way to say this is that one column in a hex number is the
same as four columns of a binary number.
0
1
2
1
2
100101011011 01111010
16
16
16
16
-1
16
-2
=
0x 95B 7A*
100101011011.01111010
2
5
2
4
2
6
2
7
2
9
2
8
2
10
2
11
2
1
2
0
2
2
2
3
2
-3
2
-4
2
-2
2
-1
2
-7
2
-8
2
-6
2
-5
0x 95B.7A
*Note:
The “0x” prefix
before a number signifies
“hexadecimal ”
© N. B. Dodge 9/09
2
Lecture #2:
Signed Binary Numbers and Binary Codes
“hexadecimal
.”

Erik Jonsson School of Engineering and
Th
U i
it
f T
t D ll
Computer Science
The University of Texas at Dallas
Hexadecimal-Binary
Conversion
•
Most computers process 32 or 64 bits at a time.
–
In a 32-bit computer such as we will study, each data element in the
computer memory (or “word”) is 32 bits.
computer memory (or
word
) is 32 bits.
–
Example:
01111000101001011010111110111110
–
Separate into 4-bit groups, starting at the right:
0111 1000 1010 0101 1010 1111 1011 1110
–
Converting:
0111
2
=7
16
, 1000
2
=8
16
, 1010
2
=A
16
, 0101
2
=5
16
,
1010
2
=A
16
, 1111
2
=F
16
, 1011
2
=B
16
, 1110
2
=E
16
–
Or,
01111000101001011010111110111110 = 0x 78A5AFBE
A
th
l
•
Another example:
–
Grouping:
1001011100.11110011
2
= 10
0101
1100
. 1111
0011
= (00)10
0101
1100
. 1111
0011
=
2
5
C
F
3
= 0x 25C F3
© N. B. Dodge 9/09
3
Lecture #2:
Signed Binary Numbers and Binary Codes
=
2
5
C
.
F
3
= 0x 25C.F3

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