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BCD to Decimal - Digital Electronics
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BCD to Decimal - Digital Electronics
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 (16 + 8 + 4 + 0 + 1)10 Step 3 (11101)2 (29)10 Binary Number − 111012 = 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
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