Microsoft Word - Digital Logic Design v_4_6a

1.6. Base Conversions

 Decimal to Binary Conversion

Alternative 1 – “Subtract the weight method”
 Steps:
♦ Find the largest power of 2 (2n) that can be subtracted out of the decimal number
♦ Take the result and subtract (2n-1) from it

If the result is not negative then that bit is one

If the result is negative, then that bit is zero and the result equals the result from
step 1
♦ Repeat step 2 until the result is exactly 0

 Example: convert (49) 10 to a binary number

 Alternative 2 – “Division by 2 method”

 Steps:

♦ Divide the decimal number by 2


 Remainder is the least significant bit (most right bit)


 Quotient is used in the next step

♦ Divide quotient by 2


 Remainder is the next significant bit (next left bit)


 Quotient is used in the next step

♦ Repeat previous step until quotient is 0

 Example: convert (49) 10 to a binary number

 Binary to Decimal Conversion – “Add the weight method”

Step:
Simply multiply each bit with its weight and add to get the decimal number

 Example: Convert (110001) 2 to a decimal number

(110001) 2 = ( 1* 2^5 + 1* 2^4 + 0* 2^3 + 0* 2^2 + 0* 2^1 + 1* 2^0 ) 10 = (49) 10

 Binary ↔ Octal Conversion - “Group of 3 method”

Remainder

2|49 1 (LSB)

2|24 0

2|12 0

2| 6 0

2| 3 1

2| 1 1 (MSB)

2| 0 Stop

(49) 10  (110001) 2

49

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17

2

n



Results 

17

-

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1

Binary #  ( 1 1 0 0 0 1) 2

1

-

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-

1

-

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-

1

-

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-

1

-

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0 When =0, done

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