Conversion of number system

Conversion of Number System:

Binary conversion:

Binary to decimal: Converting binary radix to decimal radix Example   (100.01)r2 à(  )r10 = (1x10*2)+(0x10*1)+(0x10*0)+.+(0x10*-1)+(1x10*-2) = 100 + 0 + 0 + . + 0 + 0.01 =(100.01)r10

 

Binary to Octal: Converting binary radix to Octal radix Example       (10101101.0111)r2 à ()r8   Add 0 to make 3                        Add 0 to make 3 bit                                                         bit      l                                                                l   0 1 0 1 0 1 1 0 1 . 0 1 1 1 0 0 2 5 5 3 4

 

 

 

Binary to Hexadecimal: Converting binary radix to Hexadecimal radix Example       (1101101110.1001101)r2 à ()r16   Add 0 to make 4                        Add 0 to make 4 bit                                                         bit     l                                                                                    l 0 0 1 1 0 1 1 0 1 1 1 0 . 1 0 0 1 1 0 1 0 3 6 E 9 A

 

Octal conversion:

Octal to binary:  Converting octal radix to binary radix. Example:     (125.62)r8 à ( )r2 1 2 5 . 6 2 0 0 1 0 1 0 1 0 1 1 1 0 0 1 0  l___l           1    0      1   0   1      0   1  .      1  1  0     0  1  0     l remove the extra     zeros

 

 

Octal to Hexadecimal: Converting Octalradix to Hexadecimal radix. Example: (615.25)r8 à ( )16 Step 1: convert the octal to binary first  Step 2: again convet the binary to Hexadecimal. 6 1 5 . 2 5   1 1 0 0 0   1   1 0 1 . 0 1 0 1 0 1   0001 1000 1101   0101 0100   1 8 D . 5 4

Octal to decimal Converting octal radix to decimal radix. Example:  (623)r8 à ( )r10 =(6x8*2)+(2x8)+3 =(403)r10

 

 Hexadecimal conversion:

Hexadecimal to binary: Converting Hexadecimal radix to binary radix  Example    (549.B4)r16 à ()r2     5 4 9 . B 4 0 1 0 1 0 1 0 0 1 0 0 1 . 1 0 1 1 0 1 0 0 0 1 0 1 0 1 0 0 1 0 0 1 . 1 0 1 1 0 1 - -                                                                            Trailing zeros (10101001001.101101)r2

 

Hexadecimal to decimal:   Converting Hexadecimal radix to decimalradix     Example: (A23)r16 à ()r10     (Ax16*2)+(2x16)+(3) = (291)r10

 

Hexadecimal to Octal: Converting Hexadecimal radix to Octal  radix. Example: Step 1: convert the hexadecimal to binary  Step 2: then convert to octal   B C 6 6 . A F 1011 1100 0110 0110 . 1010 1111 001 011 110 001 100 110 . 101 011 110 1 3 6 1 4 6 . 5 3 6 *adding extra zeros to make it 3 bit

 

   Decimal conversion:

Decimal to binary: Converting decimal radix to binary  radix.    Example: (12.125)r16 à ( )r2    12 / 2 = 6   0        6 / 2 =  3    0                                  *- Quotient    3 / 2 = 1      1                                  *- Remainder    1 / 2  = 0     1          Answer  1100  (*move the remainder in upward direction to         get a correct answer)

 

Decimal to octal: Converting decimal radix to octal  radix.    Example: (658.825)r16 à ( )r8    658 / 8 = 82   2        82 / 8 =  10    2                                  *- Quotient    10 / 8 = 1     2                                  *- Remainder    1 / 8  = 0    1          Answer  1222  (*move the remainder in upward direction to         get a correct answer)

 

Decimal to Hexadecimal: Converting decimal radix tohexadecimal  radix. Example: (5386.345)r10 à ( )r16 5386 / 16 = 336   10     336 / 16 =  21       0                                  *- Quotient 21 / 16 = 1            5                                  *- Remainder 1 / 16  = 0             1       Answer  150A  (*move the remainder in upward direction to get a correct answer)

 

Digital logic circuit

Unit 1

Representation of number of different Radix

Conversion of number system

Binary Arithmetic

Binary codes

Error detection and correction codes

Characteristics of digital logic families

RTL

DTL

TTL

MOS Families

ECL

Comparison between families