The document discusses different number systems including binary, decimal, octal, and hexadecimal. It provides details on:
- How each system uses different digits or "radix" (e.g. binary uses 0 and 1)
- Converting between the different number systems by grouping digits and representing them in other bases
- Methods for converting integers and fractions between decimal and other number systems using successive division or multiplication.
2. Binary Number System
•A system uses only the digits 0 and 1 as codes.
• The word ‘bit’ is the abbreviation for binary digit.
• The binary number has 4 bits i.e. 0000 or 1111 called as nibble.
• The binary number with 8 bits i.e. 00000000 or 11111111 called as
byte.
15. • Group into 3's starting at least significant symbol (if the
number of bits is not evenly divisible by 3, then add 0's at the
most significant end)
•write 1 octal digit for each group
e.g.: (1010101)2 to ( )8
001 010 101
1 2 5
Answer= 1258
Binary to Octal
17. Binary to Hexadecimal
• Group into 4's starting at least significant symbol (if the
number of bits is not evenly divisible by 4, then add 0's at
themostsignificantend)
•write 1 hex digit for each group.
e.g.:(1010111011)2to ()16
10 1011 1011
B
2 B
Answer= (2BB)16
18. Hexadecimal to Binary
• For each of the Hex digit write its binary equivalent (use 4 bits to
represent).
e.g.: (25A0)16to ()2
25A0
0010
0101 1010
0000
Answer= (0010010110100000)2
19. • Steps:
1.Convertoctalnumberto itsbinary equivalent
2.Convertbinarynumberto itshexadecimalequivalent
e.g.: (635.27)8 to ()16
6 3 5 . 2 7
110 011 101 . 010 111
000 00
1 9 D . 5 C
Octal to Hexadecimal
22. Decimal to Any Base
Steps:
1. Convertintegerpart
( SuccessiveDivisionMethod )
2. Convertfractionalpart
( SuccessiveMultiplicationMethod )
23. Stepsin SuccessiveDivisionMethod
1. Dividetheintegerpartof decimalnumberbydesired
basenumber,storequotient(Q) andremainder(R)
2. Consider quotient as a new decimal number
and repeatstep1untilquotientbecomes 0
3. Listtheremaindersin thereverse order
Stepsin SuccessiveMultiplicationMethod
1. Multiply the fractional part of decimal number by
desiredbasenumber
2. Record the integer part of product as carry and
fractionalpartasnewfractional part
3. Repeat steps 1 and 2 until fractional part of product
becomes0or untilyouhavemanydigitsasnecessary for
yourapplication
4. Readcarriesdownwardsto getdesiredbasenumber