NUMBER SYSTEMS:
BINARY, DECIMAL,
HEXADECIMAL AND
OCTAL.
CONVERSION
BETWEEN VARIOUS
NUMBER SYSTEMS
,DECIMAL NUMBERS
• In the decimal number systems each of the ten digits, 0
through 9, represents a certain quantity. The position of
each digit in a decimal number indicates the magnitude of
the quantity represented and can be assigned a weight. The
weights for whole numbers are positive powers of ten that
increases from right to left, beginning with 10º = 1
• ……………10 10 10³ 10² 10¹ 10º
• For fractional numbers, the weights are negative powers of
ten that decrease from left to right beginning with 10¯¹.
• 10² 10¹ 10º . 10¯¹ 10¯² 10¯³ ……..
• The value of a decimal number is the sum of digits after each
digit has been multiplied by its weights as in following
examples.
, BINARY NUMBERS
• The binary system is less complicated than the decimal system
because it has only two digits, it is a base-two system. The two binary
digits (bits) are 1 and 0. The position of a 1 or 0 in a binary number
indicates its weight, or value within the number, just as the position of
a decimal digit determines the value of that digit. The weights in a
binary number are based on power of two as:
• ….. 2 2³ 2 2 2º . 2¯ 2¯……….
• With 4 digits position we can count from zero to 15.In general, with n
bits we can count up to a number equal to 2ⁿ - 1.
• Largest decimal number = 2ⁿ - 1
BINARY, DECIMAL,
HEXADECIMAL AND
OCTAL.
CONVERSION
BETWEEN VARIOUS
NUMBER SYSTEMS
,DECIMAL NUMBERS
• In the decimal number systems each of the ten digits, 0
through 9, represents a certain quantity. The position of
each digit in a decimal number indicates the magnitude of
the quantity represented and can be assigned a weight. The
weights for whole numbers are positive powers of ten that
increases from right to left, beginning with 10º = 1
• ……………10 10 10³ 10² 10¹ 10º
• For fractional numbers, the weights are negative powers of
ten that decrease from left to right beginning with 10¯¹.
• 10² 10¹ 10º . 10¯¹ 10¯² 10¯³ ……..
• The value of a decimal number is the sum of digits after each
digit has been multiplied by its weights as in following
examples.
, BINARY NUMBERS
• The binary system is less complicated than the decimal system
because it has only two digits, it is a base-two system. The two binary
digits (bits) are 1 and 0. The position of a 1 or 0 in a binary number
indicates its weight, or value within the number, just as the position of
a decimal digit determines the value of that digit. The weights in a
binary number are based on power of two as:
• ….. 2 2³ 2 2 2º . 2¯ 2¯……….
• With 4 digits position we can count from zero to 15.In general, with n
bits we can count up to a number equal to 2ⁿ - 1.
• Largest decimal number = 2ⁿ - 1
