Number System Conversions

1
Number System Conversions

• Lecture L2.2
• Section 2.3

2
Number System Conversions

• Hex, Binary, and Octal to Decimal
• Binary Hex
• Binary Octal
• Hex Octal
• Decimal to Hex, Octal, and Binary

3
Hex to Decimal
8 7 C 9 x 16 128 7 135 x 16
2,160 12 2,172 x 16 34,752 9 34,761
4
Binary Hex
0110 1010 1000 . 1111 0101 1100
6 A 8 . F 5 C
5
Binary Octal
011 010 101 000 . 111 101 011 100
3 2 5 0 . 7 5 3 4
6
Hex OctalGo through Binary
0110 1010 1000 . 1111 0101 1100
6 A 8 . F 5 C
011 010 101 000 . 111 101 011 100
3 2 5 0 . 7 5 3 4
7
Convert Decimal to any Base
Integer Part Divide by the base, keep track of
the remainder, and read up.
16 34,761 16 2,172 rem 9 16 135 rem 12 C
16 8 rem 7 0 rem 8
34,76110 87C916
8
Convert Decimal to any Base
Fractional Part Multiply by the base, keep
track of the integer part, and read down.
0.78125 x 16 12.5 int 12 C 0.5 x 16
8.0 int 8
0.7812510 C816
9
Convert Decimal to any Base
Fractional Part Multiply by the base, keep
track of the integer part, and read down.
0.1 x 2 0.2 int 0 0.2 x 2 0.4 int
0 0.4 x 2 0.8 int 0 0.8 x 2 1.6 int
1 0.6 x 2 1.2 int 1 0.2 x 2 0.4 int
0 0.4 x 2 0.8 int 0
0.110 0.000112
10
Questions
10010101
? (decimal)
2
11
Questions
85710 ?16
12
Questions
BED
?
16
2