# Codes Conversion

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 (0110)BCD to Excess-3.

(0110)BCD = 610

### Step 2 − Add 3 to decimal

(6)10 + (3)10 = (9)10

### Step 3 − Convert to Excess-3

(9)10 = (1001)2

Result

```(0110)BCD = (1001)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   = 1 0 0 1 0 1 1 1
--------------------
BCD = 0 1 1 0   0 1 1 1
```

Result

```(10011010)XS-3 = (01100111)BCD
```