Binary Hex Decimal 2 3 4 5 - New Mexico Institute of Mining and Technology
EE 308
Spring 2002
Binary, Hex and Decimal Numbers (4-bit representation)
Binary
0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111
Hex Decimal
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
1
EE 308
Spring 2002
What does a number represent?
Binary numbers are a code, and represent what the programmer intends for the code.
0x72
Some possible codes:
'r' (ASCII) INC (HC12 instruction) 2.26V (Input from A/D converter) 11410 (Unsigned number) 11410 (Signed number) Set temperature in room to 69 F Set cruise control speed to 120 mph
2
EE 308
Spring 2002
Binary to Unsigned Decimal:
Convert Binary to Unsigned Decimal 1111011 2
6
5
4
1x2 +1x2 +1x2
+
1
x
3
2+
0
x
2
2+
1
x
1
2
+
1
x
20
1 x 64 + 1 x 32 + 1 x 16 + 1 x 8 + 0 x 4 + 1 x 2 + 1 x 1
123
10
Hex to Unsigned Decimal Convert Hex to Unsigned Decimal 82D6 16
3
8 x 16
+ 2 x 16 2 + 13 x 16 1 + 6 x 16 0
8 x 4096 + 2 x 256 + 13 x 16 + 6 x 1
33494
10
3
EE 308
Unsigned Decimal to Hex
Convert Unsigned Decimal to Hex
Spring 2002
Division Q
721/16
45
45/16
2
2/16
0
R
Decimal Hex
1
1
13
D
2
2
721 = 2D1
10
16
4
EE 308
Unsigned Number Line: Numbers go from 0 to
Spring 2002
0 1 2 2 42 5 6 7 8 9 10 11 12 13
Unsigned Number Line
??????? Unsigned Number Wheel: Numbers go from 0 to
01234567 0
7
1
000
111
001
6
110
010
2
101
011
100
5
3
4
5
................
................
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