What is decimal number system? The **decimal number system** has base 10. It uses the digits 0 to 9. What is number system? It is a system for representing numeric values or quantities using different symbols i.e. digits. What does base or radix mean? The number of digits (symbols) a number system use is called base or radix of that number system.

What is binary number system? The **binary number system** has base 2. It uses the digits 0 and 1 only. How we write a binary number? We can write a binary number as (1010)2 because its base is 2.

**Method of Conversion for Binary & Decimal Numbers**

Which method is best to **convert a decimal number in to binary numbers?**

To convert a decimal number into binary number we use Division method.

Which method is used to convert a binary numbers into decimal number?

To convert a binary number into decimal number we use Expansion method.

## Decimal to Binary Conversion Method

i. Divide the number by 2.

ii. Put the reminder on right side.

iii. Keep dividing the quotient till we get the quotient less than 2.

iv. Record reminders from bottom to top to get the answer.

Example: (21)10 = (10101)2

Activity:

Convert (31)10 into its binary equivalent. Answer should be (11111)2

**Place Value & Decimal to Binary Conversion**

What is the place value of 2 in (1259)10? The place value of 2 in (1259)10 is 2×100 = 2×10^{2}= 200. Now lets see how we can convert a binary number in to decimal number using expansion and place value method.

i. Multiply each digit with its place value.

ii. Add these place values.

iii. The sum is a decimal number.

Example: (11101)2=(1×2^{4})+ (1×2^{3})+(1×2^{2})+(0×2^{1})+(1×2^{0})=(1×16)+ (1×8) +(1×4)+ (0×2)+(1×1)= 16 + 8 + 4 + 0 + 1 = 29

Answer: (11011)2 = (29)10

Activity:

Convert (11011)2 into its decimal equivalent. Answer should be (27)10

### What is BCD?

Binary coded decimal (BCD) is a system of writing numerals that assigns a four-digit binary code to each digit 0 through 9 in a decimal (base-10) numeral. The four-bit BCD code for any particular single base-10 digit is its representation in binary notation, as follows:

0 = 0000.

1 = 0001.

2 = 0010.

Numbers larger than 9, having two or more digits in the decimal system, are expressed digit by digit in binary coded decimal. For example, the BCD rendition of the base-10 number 1895 is 0001 1000 1001 0101. The binary equivalents of 1, 8, 9, and 5, always in a four- digit format, go from left to right. The BCD representation of a number is not the same, in general, as its simple binary representation. In binary form, for example, the decimal quantity 1895 appears as 11101100111.

## Binary to Decimal to BCD Conversion Example

**Binary Coded Decimal** which is also called as BCD is another process for converting decimal numbers into their binary equivalents.

**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 from Binary Number

(11101)2 = (1×2^{4})+ (1×2^{3})+(1×2^{2})+(0×2^{1})+(1×2^{0})=(1×16)+ (1×8) +(1×4)+ (0×2)+(1×1)= 16 + 8 + 4 + 0 + 1 = (29)10

Step 2 : Convert to BCD from Decimal Number = (29)10 Calculating BCD Equivalent. Convert each digit into groups of four binary digits equivalent.

Decimal Number Conversion

(29)10 = (0010)2 (1001)2

(29)10 = (00101001) BCD

Therefore 0010 1001 is the **BCD code** for decimal 29.

BCD numbering system is very easy to understand, while creating BCD each decimal number is separated into equivalent four bits for each decimal digit within the number. In the final result each decimal digit is replaced by its weighted binary value performing a direct translation of the number. Every 4-bit group represents each displayed decimal digit from 0000 for a zero to 1001 for a nine. For example:

357_{10} (Three Hundred and Fifty Seven) in decimal would be presented in Binary Coded Decimal as:

357_{10} = 0011 0101 0111 (resulted BCD)

### Binary to Decimal Conversion Video Guide

Below is very simple video presentation that shows in two minutes how to convert a binary number to its equivalent decimal number.

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Thank you very much. The way of converting the binary to decimal and decimal to binary is wel explained. Is there any video for this.