# Bab 1

Topics: Binary numeral system, Hexadecimal, Decimal Pages: 22 (1519 words) Published: April 2, 2013
Digital
Digital Electronics
(EE202)
(EE202)

NUMBER
NUMBER SYSTEMS
• Decimal

0~9

• Binary

0~1

• Octal

0~7

0~F

DECIMAL
DECIMAL
The decimal system is composed of 10
numerals or symbols. These 10 symbols
are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9; using these
symbols as digits of a number, we can
express any quantity. The decimal
system, also called the base-10 system
because it has 10 digits.

EXAMPLE:
47 = (4 X 101)+(7 X 100)
= (4 X 10) + (7 X 1)
= 40+ 7
EXERCISE :
568.23 =

BINARY
BINARY
In the binary system, there are only two
symbols or possible digit values, 0 and 1.
This base-2 system can be used to
represent any quantity that can be
represented in decimal or other number
system.

Binary
Binary to decimal conversion
23

22

21

20

Decimal

0

0

0

0

0

0

0

0

1

1

0

0

1

0

2

0

0

1

1

3

0

1

0

0

4

0

1

0

1

5

0

1

1

0

6

0

1

1

1

7

Dan
seterusnya…
……..

……

……..

…….

8

Example 1:
Convert the binary whole number
110112 to decimal.
Weight :
Binary number :

24 23 22 21 20
1 1 0 1 12
= 16+8+0+2+1
= 2710 (decimal)

Example 2:
Convert the fractional number
0.10112 to decimal.
Weight :
2-1 2-2 2-3 2-4
Binary number : 0. 1 0 1 12
=0.5+0+0.125+0.0625
= 0.687510

Decimal
Decimal to binary conversion
Using methods:

Convert a decimal number to binary using
Sum-of-weight method

Convert a decimal whole number to binary
using the repeated devison-by-2 method

Convert a decimal fraction to binary using
the repeated multiplication-by-2 method

Sum-ofSum-of-weight method
Find binary weights that add up to
decimal number.
Example:
Convert the decimal number 9 to binary
9= 8+1
23

22

21

20

8

4

2

1

1

0

0

1

Binary number for decimal is 1001

Repeated devison-byRepeated devison-by-2 method
Divide decimal number by 2 until the quotient is
0. Remainder form the binary number.
Example: Converting decimal number 25 to
binary.

Stop when the
whole-number
quotient is 0

Repeated multiplication-byRepeated multiplication-by-2
method
Example: Convert the decimal fraction 0.3125 to
binary

Continue to the
desired number
of decimal
places or stop
when the
fraction part is
all zeros.

Exercise:
Exercise:
1.
2.

3.
4.

Convert the following decimal numbers to
binary 12,58,82
Convert each decimal number to binary by
using the repeated division-by-2
method(repeated multiplicatio-by-2 for
fraction)
fraction)
a)21
b)0.375
Convert the following octal numbers to decimal
a)738
b)1258
Convert the following decimal numbers to octal
a)9810 b)16310

OCTAL
OCTAL
The octal number system has a base of
eight, meaning that it has eight possible
digits: 0,1,2,3,4,5,6,7.

Octal
Octal conversion
Octal to decimal conversion
2. Decimal to Octal conversion
3. Octal-To-Binary Conversion
4. Binary-To-Octal conversion
1.

Octal
Octal to decimal conversion
Example : Convert the octal number
23748 to decimal.
Weight : 83 82 81 80
Octal number : 2 3 7 4
2374
23748= (2x 83)+(3x 82)+(7x 81)+(4x 80)
= 1024+192+56+4
=127610

1.

Decimal
Decimal to octal conversion
A method of converting a decimal number
to an octal number is the repeated divisionby-8 method.
1. Example 1: Convert the decimal number
359 to octal.
359/8 =44.875

0.875x 8

=7 LSD

44 /8 =5.5

0.5 x 8

=4

5

0.625 x 8 =5 MSD
=547 octal number

/8 =0.625

Stop when whole number
quotient is zero

Octal-ToOctal-To-Binary Conversion
Because each octal digit can be
represented by a 3-bit binary number, it is
very easy to convert from octal to binary.
Each octal digit is represented by three bit
as
as shown in table below:
Octal
Digit

0

1

2

3

4

5

6

7

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