Codes Conversion

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There are many methods or techniques which can be used to convert code from one format to another. We'll demonstrate here the following

  • Binary to BCD Conversion

  • BCD to Binary Conversion

  • BCD to Excess-3

  • Excess-3 to BCD

Binary to BCD Conversion

Steps

  • Step 1 -- Convert the binary number to decimal.

  • Step 2 -- Convert decimal number to BCD.

Example: convert (11101)2 to BCD.

Step 1 - Convert to Decimal

Binary Number: 111012

Calculating Decimal Equivalent:

StepBinary NumberDecimal Number
Step 1111012((1 x 24) + (1 x 23) + (1 x 22) + (0 x 21) + (1 x 20))10
Step 2111012(16 + 8 + 4 + 0 + 1)10
Step 31110122910

Binary Number: 111012 = Decimal Number: 2910

Step 2 - Convert to BCD

Decimal Number: 2910

Calculating BCD Equivalent. Convert each digit into groups of four binary digits equivalent.

StepDecimal NumberConversion
Step 1291000102 10012
Step 2291000101001BCD

Result

(11101)2 =  (00101001)BCD

BCD to Binary Conversion

Steps

  • Step 1 -- Convert the BCD number to decimal.

  • Step 2 -- Convert decimal to binary.

Example: convert (00101001)BCD to Binary.

Step 1 - Convert to BCD

BCD Number: (00101001)BCD

Calculating Decimal Equivalent. Convert each four digit into a group and get decimal equivalent or each group.

StepBCD NumberConversion
Step 1(00101001)BCD00102 10012
Step 2(00101001)BCD210 910
Step 3(00101001)BCD2910

BCD Number: (00101001)BCD = Decimal Number: 2910

Step 2 - Convert to Binary

Used long division method for decimal to binary conversion.

Decimal Number: 2910

Calculating Binary Equivalent:

StepOperationResult Remainder
Step 129 / 2141
Step 214 / 270
Step 37 / 231
Step 43 / 211
Step 51 / 201

As mentioned in Steps 2 and 4, the remainders have to be arranged in the reverse order so that the first remainder becomes the least significant digit (LSD) and the last remainder becomes the most significant digit (MSD).

Decimal Number: 2910 = Binary Number: 111012

Result

(00101001)BCD = (11101)2

BCD to Excess-3

Steps

  • Step 1 -- Convert BCD to decimal.

  • Step 2 -- Add (3)10 to this decimal number.

  • Step 3 -- Convert into binary to get excess-3 code.

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

(1001)BCD = (1100)XS-3

Excess-3 to BCD Conversion

Steps

  • Step 1 -- Subtract (0011)2 from each 4 bit of excess-3 digit to obtain the corresponding BCD code.

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

Given XS-3 number       =  1 0 0 1  1 0 1 0

Subtract (0011)2             =  0 0 1 1  0 0 1 1

                                              --------------------

                                  BCD = 0 1 1 0 0 1 1 1

Result

(10011010)XS-3 = (01100111)BCD


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