Number system conversion
In this
section, we will only focus in number system conversion of decimal, binary,
octal and hexadecimal.
Decimal to
binary
Example :Convert
decimal number 33.875 to binary number.
weight
|
25
|
24
|
23
|
22
|
21
|
20
|
2-1
|
2-2
|
2-3
|
value
|
32
|
16
|
8
|
4
|
2
|
1
|
0.5
|
0.25
|
.0125
|
binary
|
1
|
0
|
0
|
0
|
0
|
1
|
1
|
1
|
1
|
33.875 1.875 0.875 0.375 0.125
-32.0 -1.000 -0.500 -0.250 -0.125
1.875 0.875 0.375 0.125 0
So, 33,87510
= 100001.1112
Decimal to
octal
Convert decimal
65.140625 to octal
weight
|
82
|
81
|
80
|
8-1
|
8-2
|
value
|
64
|
8
|
1
|
0.125
|
0.015625
|
hexadecimal
|
1
|
0
|
0
|
1
|
1
|
65.140625 1.140625 0.140625 0.015625
-64.000000 -1.000000 -0.125000 -0.015625
1.140625 0.140625 0.015625 0
Decimal to Hexadecimal
Convert
decimal 272.0625 to hexadecimal
weight
|
162
|
161
|
160
|
16-1
|
value
|
256
|
16
|
1
|
0.0625
|
hexadecimal
|
1
|
1
|
0
|
1
|
272.0625 16.0625 0.0625
-256.0000 -16.0000 -0.0625
16.0625 0.0625 0
Binary to octal
To convert to octal use 3 digit,
Example:
1110101110.1012
= 001 110 010 110 . 1012 = 1626.58
1 6 2
6 5
Binary to hexadecimal
To convert to hexadecimal use 4
digit,
Example:
1110101110.1012
= 0011 1001 0110
. 10102 = 396.A16
3 9 6 10
As the same way to convert from
octal, hexadecimal to binary.
Octal to binary
Example:
470.538 = 4 7 0 . 5 3
=100111000.1010112
100
111 000 101 011
2’s complement
Step to
convert to 2’s complement:
Step 1:
change octal, decimal or hexadecimal to binary.
Step
2:change 0 become 1 and 1 become 0.At this step, number is 1’s complement.
Example:
00001100(12) à 11110011
11110001(114) à 00001110
00000010(2) à 11111101
Step 3: 1’
complement +1. The final value is 2’ complement
11110011+1=11110100 (-12)
00001110 + 1 = 00001111 (-144)
11111101+1=11111110 (-2)
Example:
convert (-27) to 2’s complement
For using
8-bits, the number 27 is represented by
000110112
Then convert
1 to 0, 0 to 1,
11100100
Adding 1 at
the final step,
11100101 = -27
How to
differentiate positive / negative number in binary???
Use the
most left bit as the sign bit, 0 will represent to positive number,1 will represent
to negative number.
0010
= 2 1110 = -
2
Two's
complement
|
Decimal
|
0111
|
7
|
0110
|
6
|
0101
|
5
|
0100
|
4
|
0011
|
3
|
0010
|
2
|
0001
|
1
|
0000
|
0
|
1111
|
−1
|
1110
|
−2
|
1101
|
−3
|
1100
|
−4
|
1011
|
−5
|
1010
|
−6
|
1001
|
−7
|
1000
|
−8
|
Sign bit
repetition in 7-bit and 8-bit integers using 2’s complement
Decimal
|
7-bit notation
|
8-bit notation
|
8
|
0001000
|
00001000
|
-8
|
1111000
|
11111000
|
32
|
0100000
|
00100000
|
-32
|
1100000
|
11100000
|
8-bit two's-complement integers
Bits
|
Unsigned value
|
2's complement value
|
00000000
|
0
|
0
|
00000001
|
1
|
1
|
00000010
|
2
|
2
|
01111110
|
126
|
126
|
01111111
|
127
|
127
|
10000000
|
128
|
−128
|
10000001
|
129
|
−127
|
10000010
|
130
|
−126
|
11111110
|
254
|
−2
|
11111111
|
255
|
−1
|
Why 1111(8) does not involve in 4 bit?
Because it is 4-bit number, the most positive 4-bit number is 0111(7),
the most negative
is 1000(-8).
8 is too large to represent in 4-bit . Therefore, the most positive is 7 (0111).
Kee Hwaai Sziang B031210067
No comments:
Post a Comment