This document describes how to convert a Binary Coded Decimal (BCD) number to its equivalent binary number. It explains that BCD represents decimal numbers as 4-bit binary codes, with values 0-9 having their own codes. For values above 9, each decimal digit is represented by a 4-bit code. The document includes a truth table and Karnaugh maps to derive the logic gates needed for a BCD to binary converter circuit. It also notes that for BCD values above 9, the most significant bits in the binary output are "don't cares".

1. BCD to Binary converter
BY
G.KIRUTHIKAMANI

2. Introduction
BCD refers to Binary Coded Decimal.
BCD is a way of representing digital numbers as a string of
bits suitable for electronic systems
It is fast and efficient system to convert decimal to binary
system compared to pure binary system
BCD is a self complimenting code

3. BCD to Binary code conversion
Here 4 bit BCD to binary number is considered.
In case of BCD number it is similar to binary till decimal
value 9
After 9,each digit of decimal representation takes 4 digits in
BCD

4. BCD to Binary code conversion
Eg:
Decimal Number BCD Number Binary Number
9 1001 1001
10 00010000 1010
16 00010110 1111

5. Truth Table for BCD to Binary
number conversion
Decimal
Number
BCD Number
ABCD
Binary Number
WXYZ
0 0000 0000
1 0001 0001
2 0010 0010
3 0011 0011
4 0100 0100
5 0101 0101
6 0110 0110
7 0111 0111
8 1000 1000
9 1001 1001

6. BCD to Binary number conversion
After decimal number 9, value 10 is given by 0001 0000(BCD)
and denoted by binary number XXXX.
Value 11 is given by 00010001(BCD) denoted by binary
number XXXX and so on.
The ouputs for binary after 9 of BCD is considered as don’t
care.

7. K-map for W and X
x x x x
1 1 x x
AB
CD
00
01
11
10
00 01 11 10
1 1 1 1
x x x x
x x
AB
CD
00
01
10
00 01 11 10
W=A
11
X=B

8. K map for Y and Z
1 1
1 1
x x x x
x x
AB
CD
00
01
10
00 01 11 10
1 1
1 1
x x x x
1 x x
AB
CD
00
01
10
00 01 11 10
11
11
Y=C Z=D

9. Circuit for BCD to Binary Converter
W X Y Z
A
B
C
D