Microsoft Word - Digital Logic Design v_4_6a

 Example: Convert (52) 10 to binary (radix, r = 2)

Therefore (52) 10 = (110100) 2

 Decimal Fraction Conversion to any Base – “Repeated Radix Multiplication Method”

 Solution is based on the approach:

(decimal fraction) 10 = d -1 r--1 + d -2 r--2 + ... = (.dn...d 2 d 1 d 0 )r

r*(decimal fraction) 10 = d -1 + d-2r-1 + ... = (.d-1d-2d-3 ... )r

 Steps:

(1) Multiply (fraction) 10 by r, the non-fractional part is the first digit

(2) Continue step 2 until fraction is 0

 Example: Convert (.125) 10 to binary (r=2)

Solution:

Therefore (.125) 10 = (.001) 2

Note: Some numbers may not be fully convertible, so you have to decide the number of decimal

points you need to convert. For example (1/12) 10 does not fully convert to binary number.

.

x 2

-----

0.

d-

.

x 2

-----

0.

d-

.

x 2

-----

1.

d-

Fraction is 0 which means d -3 is the Least Significant Digit

Non-fraction portion is 1 which means d-3 is 1.

Non-fraction portion is 0 which means d-1 ,the Most Significant Digit, is 0.

52

-

----

12

-

----

0

26

2

13

(^2 )

• 
  

  ---

  
  

  1

  
  

6

(^2 )

• 
  

  ---

  
  

  0

  
  

3

2

Remainders
R 0 =d 0 =0 R 1 =d 1 =0 R 2 =d 2 =1 R 3 =d 3 =0 R 4 =d 4 =1 R 5 =d 5 =

26

-

----

06

- 6

----

0

3

-

----

1

1

(^2 )
0

1

0

2

Quotient is 0 therefore remainder is MSB

First Remainder is the LSB