1. CSE 102 Introduction to Computer Engineering
Number System

2. Number Systems Binary numbers (Base 2): 0,1
Octal numbers (Base 8): 0,1,2,3,4,5,6,7
Decimal numbers (Base 10): 0,1,2,3,4,5,6,7,8,9
Hexadecimal numbers (Base 16): 0,1,2,3,4,5,6,7,8, 9,A,B,C,D,E,F

3. Decimal to Binary Conversion
(102)10 = (?)2
= ( )2
Divide by 2
Remainder
102 2 51 25 1 12 6 3

4. Decimal to Binary Conversion
(0.125)10 = (?)2
= (0.001)2
Multiply by 2
Integer part
0.125 2
0.25
0.5
1.0 1

5. Decimal to Binary Conversion
Multiply by 2
Integer part
0.4 2
0.8
1.6 1
1.2
(0.4)10 = (?)2
= ( )2
= (0.0110)2

6. Binary to Octal and Hexadecimal Conversion
( )2 = (146)8
Hexadecimal ( )2 = (?)16
( )2 = (66)16
6 6

7. Binary to Octal and Hexadecimal Conversion
( )2 = (0.314)8
Hexadecimal ( )2 = (?)16
( )2 = (66)16

8. Representation of Integers
Signed-magnitude representation
2’s complement representation

9. Signed-magnitude Representation
sign bit
0-positive
1-negative
integer
Ex:

10. 2’s complement Representation
To find 1’s complement of a binary number change 1s to 0s and 0s to 1s
To find 2’s complement of a number add 1 to its 1’s complement
Ex: (102)10 = ( )2
1’s complement:
2’s complement:

11. 2’s complement Representation
Ex:
+10210
-10210