1. 1

2. 2
2
+1
=3
HOW THE COMPUTER GETS
THE ANSWER

3. 3
A computer understands
information composed of only zeros and
ones.
The decimal number system is
convenient for the programmer.
The computer uses binary digits for its
operation.
0
1
0
1
1
0
1
1
0
0
1
0

4. BASIC
NUMBER
SYSTEM
DECIMAL
HEXA
DECIMAL
OCTAL
BINARY
4

5. DECIMAL NUMBER SYSTEM
5
• 0,1,2,3,4,5,6,7,8,9.DIGITS
• 10BASE

6. 6
8*10
9*10
5*10
4*10
DECIMAL NUMBER 4598
0
1
2
3

7. 7
BINARY NUMBER SYSTEM
•0,1DIGITS
•2BASE

8. 8
BINARY NUMBER 1011
1*2
1*2
0*2
1*2
0
1
2
3

9. 9
HEXADECIMAL NUMBER
SYSTEM
•0,1,2,3,4,5,6,7,
•8,9,A,B,C,D,E,F.
DIGITS
•16BASE

10. 10
HEXADECIMAL NUMBER 1A5D
D*16
5*16
A*16
1*16
0
1
2
3

11. 11
OCTAL NUMBER SYSTEM
•0,1,2,3,4,
•5,6,7,8.
DIGITS
•8BASE

12. 12
OCTAL NUMBER 5273
3*8
7*8
2*8
5*8
0
1
2
3

13. 13
CONVERSIONS IN BASIC
NUMBER SYSTEM

14. 14
BINARY TO DECIMAL
• 1 0 1 0 1
BINARY
• 5 4 3 2 1
BIT
POSITION • 1*2 +0*2 +1*2
+0*2 +1*2.
MUL WITH
BASE
• 21
DECIMAL4 3 2
1 0

15. 15
HEXADECIMAL TO DECIMAL
•5A9
HEX
•3 2 1
BIT POSITION
• 5*16
+A*16
+9*16
MUL WITH
BASE
•1449
DECIMAL2
1
0

16. 16
OCTAL TO DECIMAL
•645
OCTAL
•3 2 1
BIT
POSITION
•6*8 +4*8
+5*8.
MUL WITH
BASE
•421
DECIMAL
2 1
0

17. 17
DECIMAL TO BINARY
• Q=19
• R=139 • Q=9
• R=119 • Q=4
• R=19 • Q=2
• R=04 • Q=1
• R=02 • Q=0
• R=11
LSB MSB
Divide through out by 2
DECIMAL = 39
BINARY = 100111

18. 18
DECIMAL TO HEX
• Q=2
• R=335 • Q=0
• R=22
Divide through out by 16
LSB MSB
DECIMAL = 35
HEX = 23

19. 19
DECIMAL TO OCTAL
• Q=57
• R=5461
• Q=7
• R=157
• Q=0
• R=77
Divide through out by 8
LSB MSB
DECIMAL = 461
OCTAL = 715

20. 20
BINARY TO HEXADECIMAL
BINARY
• (010111011001)
4BITS DIV
• (0101)(1101)(1001)
HEX
• (5) (D) (9) =(5D9)2 16

21. 21
BINARY TO OCTAL
BINARY
• (101111100)
3BIT DIV
• (101)(111)(100)
OCTAL
• (5) (7) (4)
=(574)
2
8

22. 22
HEXADECIMAL TO BINARY
HEX
• (5C)
EXPANSION
• (0101)(1100)
BINARY
• (01011100)16 2

23. 23
OCTAL TO BINARY
OCTAL
• (436)
EXPANSION
• (100)(011)
BINARY
• (100011)
8 2

24. 24
HEXADECIMAL TO OCTAL
• (4DF)HEX
• (0100)(1101)(1111)EXP
• (010011010000)BINARY
• (010)(011)(011)(111)3BIT DIV
• (2337)OCTAL
16
2
8

25. 25
OCTAL TO HEXADECIMAL
• (456)OCTAL
• (100)(101)(110)EXP
• (100101110)BINARY
• (0001)(0010)(1110)4BIT DIV
• (12E)HEX
8
2
16

26. 26
REPRESENTATION OF NEGATIVE
NUMBER
9’S & 10’S COMPLIMENT
• DECIMAL NUMBER SYSTEM
1’S & 2’S COMPLIMENT
• BINARY NUMBER SYSTEM

27. 27
BINARY ARITHMETIC
1
• BINARY ADDITION
2
• BINARY SUBTRACTION
3
• BINARY MULTIPLICATION
4
• BINARY DIVISION

28. 28
0 + 0 = 0
1 + 0 = 1
0 + 1 = 1
1 + 1 = 0 1 (Carry bit)
BINARYADDITION
1 1 0 1 (13 decimal)
+0 0 0 1 (+1 decimal)
1 1 1 0 (14 decimal)

29. 29
BINARY SUBTRACTION
0 ‐ 0 = 0
1 ‐ 0 = 1
0 ‐ 1 = 1 1 (Carry bit)
1 ‐ 1 = 0
1 1 0 1 (13 decimal)
+ 0 0 1 1 (-3 decimal)
1 0 1 0 (10 decimal)
Borrow

30. 30
1 0 0 0 =810
X 0 1 1 0 =610
0 0 0 0
+ 1 0 0 0
+ 1 0 0 0
+ 0 0 0 0
0 1 1 0 0 0 0 = 4810
BINARY MULTIPLICATION

31. 31
BINARY DIVISION
011 ) 0 1 1 0 0 1 0 ( 1
0 1 1
0 0 0 (0
0 0 0
0 0 0 (0
0 0 0
0 0 1 (0
0 0 0
0 1 0
Q=1000=1610
R=10= 210

32. 32
SIGNED ARITHMETIC OPERATION
MSB bit is reserved to represent the sign of
the number.
When the number is negative, the sign bit is
kept one.
When the number is positive, the sign bit is 0.
In 8-bit processor, MSB = sign bit & other 7
bits = number.
In 16-bit processor, MSB = sign bit & other
15 bits = number.

33. 33
EXAMPLES
0 0 0 0 0 1 0 1 (+5 decimal)
0 0 0 0 0 1 0 0 (+4 decimal)
0 0 0 0 1 0 0 1 (+9 decimal)
0 0 0 0 0 1 0 1 (+5 decimal)
1 0 0 0 0 0 1 0 (-2 decimal)
1 1 1 1 1 1 0 1 (1’comp of -2)
1 1 1 1 1 1 1 0 (2’s comp of -2)
0 0 0 0 0 0 1 1 (+3 decimal)
1
2
1 2 1

34. 34
BCD AND GRAY CODE

35. 35
LOGIC GATES
Logic gates perform basic logical functions.
They are fundamental building blocks of
digital integrated circuits.
Most logic gates take an input of two binary
values, and output a single value of a 1 or 0.
 Some circuits may have only a few logic
gates, while others, such as microprocessors,
may have millions of them.
There are seven different types of logic gates,
which are outlined.

36. 36

37. 37

38. 38

39. 39

40. 40

41. 41

42. 42

43. 43
FLIP-FLOPS
A flip-flop or latch is a circuit that has two
stable states and can be used to store state
information.
Each flip-flop stores one bit of information

44. 44
THANK YOU