Codes Conversion - Computer Logical Organization

What are the different methods used for converting code from one format to another?

The following are the different methods used for converting code from one format to another:

  • Binary to BCD Conversion
  • BCD to Binary Conversion
  • BCD to Excess-3
  • Excess-3 to BCD

How to convert Binary code to BCD code?

The following are the steps to convert Binary code to BCD code:

  • Step 1 – The binary number is converted to decimal.
  • Step 2 – The decimal number is converted to BCD.

Example − convert (11101)2 to BCD.

Step 1 − Convert to Decimal

Binary Number − 111012

Calculation of Decimal Equivalent is as follows:

Step
Binary Number
Decimal Number
Step 1
111012
((1 × 24) + (1 × 23) + (1 × 22) + (0 × 21) + (1 × 20))10
Step 2
111012
(16 + 8 + 4 + 0 + 1)10
Step 3
111012
2910

Hence,

Binary Number − 111012 = Decimal Number − 2910

Step 2 − Convert to BCD

Decimal Number − 2910

Calculation of BCD Equivalent is as follows:

Step
Decimal Number
Conversion
Step 1
2910
0010210012
Step 2
2910
00101001BCD

Result

How to convert BCD code to Binary code?

  • Step 1 – The BCD number is converted to decimal.
  • Step 2 – The decimal is converted to binary.

Example − convert (00101001)BCD to Binary.

Step 1 - Convert to BCD

BCD Number − (00101001)BCD

Calculation of Decimal Equivalent is as follows.The decimal equivalent is obtained by converting each four digit into a group.

Step
BCD Number
Conversion
Step 1
(00101001)BCD
0010210012
Step 2
(00101001)BCD
210910
Step 3
(00101001)BCD
2910

Hence,BCD Number − (00101001)BCD = Decimal Number − 2910

Step 2 - Convert to Binary

For converting decimal to binary, long division method is used.

Decimal Number − 2910

Calculation of Binary Equivalent is as follows:

Step
Operation
Result
Remainder
Step 1
29 / 2
14
1
Step 2
14 / 2
7
0
Step 3
7 / 2
3
1
Step 4
3 / 2
1
1
Step 5
1 / 2
0
1

The last remainder should be MDS and the first remainder should be LSD.

Hence,Decimal Number − 2910 = Binary Number − 111012

Result

How to convert BCD code to Excess-3 code?

The following are the steps to convert BCD code to Excess-3 code:

  • Step 1 – BCD is converted to decimal.
  • Step 2 -- Add 3 to the decimal number.
  • Step 3 – Excess-3 code is obtained by converting into binary.

Example − convert (1001)BCD to Excess-3.

Step 1 − Convert to decimal

(1001)BCD = 910

Step 2 − Add 3 to decimal

(9)10 + (3)10 = (12)10

Step 3 − Convert to Excess-3

(12)10 = (1100)2

Result

How to convert Excess-3 code to BCD?

The following are the steps to convert Excess-3 code to BCD:

  • Step 1 – For the corresponding BCD Code, (0011) is subtracted from each 4 bit of excess-3 digit.

Example − convert (10011010)XS-3 to BCD.

Result

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