1

2

2

+1

=3

HOW THE COMPUTER GETS

THE ANSWER

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.

01

0

1

1

0

1

1

0

0

1

0

BASIC NUMBER SYSTEM

DECIMAL

HEXA

DECIMAL

OCTAL

BINARY

4

DECIMAL NUMBER SYSTEM

5

• 0,1,2,3,4,5,6,7,8,9.DIGITS

• 10BASE

6

8*10

9*10

5*104*10

DECIMAL NUMBER 4598

0

1

2

3

7

BINARY NUMBER SYSTEM

•0,1DIGITS

•2BASE

8

BINARY NUMBER 1011

1*2

1*20*2

1*2

0

1

2

3

9

HEXADECIMAL NUMBER

SYSTEM

•0,1,2,3,4,5,6,7,

•8,9,A,B,C,D,E,F.DIGITS

•16BASE

10

HEXADECIMAL NUMBER 1A5D

D*16

5*16

A*161*16

0

1

2

3

11

OCTAL NUMBER SYSTEM

•0,1,2,3,4,

•5,6,7,8.DIGITS

•8BASE

12

OCTAL NUMBER 5273

3*8

7*82*8

5*8

0

1

2

3

13

CONVERSIONS IN BASIC

NUMBER SYSTEM

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

HEXADECIMAL TO DECIMAL

•5A9

HEX

•3 2 1

BIT POSITION• 5*16

+A*16 +9*16

MUL WITH BASE

•1449

DECIMAL2

1

0

16

OCTAL TO DECIMAL

•645

OCTAL

•3 2 1

BIT POSITION •6*8 +4*8

+5*8.

MUL WITH BASE

•421

DECIMAL2 1

0

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

DECIMAL TO HEX

• Q=2

• R=335• Q=0

• R=22

Divide through out by 16

LSB MSB

DECIMAL = 35

HEX = 23

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

BINARY TO HEXADECIMAL

BINARY

• (010111011001)

4BITS DIV

• (0101)(1101)(1001)

HEX

• (5) (D) (9) =(5D9)2 16

21

BINARY TO OCTAL

BINARY

• (101111100)

3BIT DIV

• (101)(111)(100)

OCTAL

• (5) (7) (4) =(574)

2

8

22

HEXADECIMAL TO BINARY

HEX

• (5C)

EXPANSION

• (0101)(1100)

BINARY

• (01011100)16 2

23

OCTAL TO BINARY

OCTAL

• (436)

EXPANSION

• (100)(011)

BINARY

• (100011)8 2

24

HEXADECIMAL TO OCTAL

• (4DF)HEX

• (0100)(1101)(1111)EXP

• (010011010000)BINARY

• (010)(011)(011)(111)3BIT DIV

• (2337)OCTAL

16

2

8

25

OCTAL TO HEXADECIMAL

• (456)OCTAL

• (100)(101)(110)EXP

• (100101110)BINARY

• (0001)(0010)(1110)4BIT DIV

• (12E)HEX

8

2

16

26

REPRESENTATION OF NEGATIVE

NUMBER

9’S & 10’S COMPLIMENT

• DECIMAL NUMBER SYSTEM

1’S & 2’S COMPLIMENT

• BINARY NUMBER SYSTEM

27

BINARY ARITHMETIC

1• BINARY ADDITION

2• BINARY SUBTRACTION

3• BINARY MULTIPLICATION

4• BINARY DIVISION

28

0 + 0 = 0

1 + 0 = 1

0 + 1 = 1

1 + 1 = 0 1 (Carry bit)

BINARY ADDITION

1 1 0 1 (13 decimal)

+0 0 0 1 (+1 decimal)

1 1 1 0 (14 decimal)

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

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

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

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

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

BCD AND GRAY CODE

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

37

38

39

40

41

42

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

THANK YOU