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 −

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

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.

Step	Decimal Number	Conversion
Step 1	2910	00102 10012
Step 2	2910	00101001BCD

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 for each group.

Step	BCD Number	Conversion
Step 1	(00101001)BCD	00102 10012
Step 2	(00101001)BCD	210 910
Step 3	(00101001)BCD	2910

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 −

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

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