3. Radix Numbers
• Base 2 (Binary)
- 0, 1
• Base 8 (Octal)
- 0, 1, 2, 3, 4, 5, 6, 7
• Base 10 (Decimal)
- 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
• Base 16 (Hexadecimal)
– 0, 1, 2, 3 , …, 8, 9, A, B, C, D, E, F
4. Base Conversion
Base X to Base 10 (Decimal)
– Starting from the last digit, multiply
that digit by X0
– Increase the power of X by 1 and
repeat until you have done all digits
– Sum up the results
6. Base Conversion (cont.)
Base 10 (Decimal) to any base X
– Divide the number by X.
– Write down the remainder.
– Repeat the previous two steps until
the result is 0.
– The actual result is the digit sequence
of the remainders from the last to first.
8. Base Conversion (cont.)
Base 2 (Binary) to Base 8 (Octal)
– Group 3 digits from the right side
– Convert each group to its octal
representation
Do you think that number in base 2 can
also be converted to Base 16
(Hexadecimal) directly somehow?
18. Boolean expression
Boolean expression is
D = (A + B)’
E = B ∙ C
Q = D + E
= (A + B)’+(B ∙ C)
NOT (A OR B)
B AND C
D OR E
(NOT (A OR B)) OR (B AND C)
19. Truth table
Input
Output
A
B
C
D
(A + B)’
E
(B ∙ C )
Q
((A + B)’+(B ∙ C) )
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
20. Give it a try!
Find the Boolean expression and
the truth table of this circuit.
21. Give it a try!
Draw a circuit this Boolean expression:
X = ((A
B) + (C’∙ D))’
E