BCD to Decimal - Digital Electronics

This document contains
> What is BCD?
> What is Decimal?
> Steps to convert Decimal to BCD.

1. DECIMAL TO BCD
CONVERSION
by
Milap Bhanderi
Subject: Basic Electronics
Institute: Silver Oak College of Engineering and Technology.
Copyright © 2017 by Milap Bhanderi

2. What is BCD?
v 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.
v 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.
Copyright © 2017 by Milap Bhanderi

3. Number Binary
0 0000
1
0001
2 0010
3 0011
4 0100
5 0101
6 0110
7 0111
8 1000
9 1001
Copyright © 2017 by Milap Bhanderi

4. • Numbers larger than 9, having two or more digits in the
decimal system, are expressed digit by digit. 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

Copyright © 2017 by Milap Bhanderi

5. What is DECIMAL?
v A number system that uses a notation in which
each number is expressed in base 10 by using
one of the first nine integers or 0 in
each place and leXing each place value be a
power of 10.
Copyright © 2017 by Milap Bhanderi

6. Decimal Binary Octal
Hexadecima
l
1 1 1 1
2 10 2 2
3 11 3 3
4 100 4 4
5 101 5 5
6 110 6 6
7 111 7 7
8 1000 10 8
9 1001 11 9
10 1010 12 A
11 1011 13 B
12 1100 14 C
13 1101 15 D
14 1110 16 E
15 1111 17 F
16 10000 20 10
17 10001 21 11
Copyright © 2017 by Milap Bhanderi

7. DECIMAL TO BCD CONVERSION
q  Step 1 : Convert the binary
number to decimal.

q  Step 2 : Convert decimal number
to BCD.
Copyright © 2017 by Milap Bhanderi

8. Example : Convert (11101)
2
to BCD.

Step 1 : Convert to Decimal Binary Number = (11101)
2


Step Binary Number Decimal Number
Step 1 (11101)
2
( (1 × 2
4
) + (1 × 2
3
) + (1 × 2
2
) + (0
× 2
1
) + (1 × 2
0
) )
10
Step 2 (11101)
2
(1 + 8 + 4 + 0 + 1)
10
Step 3 (11101)
2
(29)
10
Binary Number − 11101
2
= Decimal Number − (29)
10
Copyright © 2017 by Milap Bhanderi

9. Step 2 : Convert to BCD Decimal Number = (29)
10

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

Step
Decimal Number Conversion
Step 1 (29)
10
(0010)
2
(1001)
2
Step 2 (29)
10
(00101001)
BCD
(11101)
2
= (00101001)
BCD
Copyright © 2017 by Milap Bhanderi

10. Copyright © 2017 by Milap Bhanderi