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BCD to Decimal - Digital Electronics

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Milap Bhanderi
Milap Bhanderi

The document discusses decimal to binary coded decimal (BCD) conversion. It defines BCD as a 4-bit coding system that represents each decimal digit with a unique 4-bit binary pattern. Numbers larger than 9 are represented by grouping the 4-bit codes for each digit from left to right. The document then provides examples of converting a binary number to decimal, and then to BCD, which involves first converting the binary number to decimal, then coding each decimal digit as a 4-bit BCD pattern.

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DECIMAL TO BCD CONVERSION by Milap Bhanderi Subject: Basic Electronics Institute: Silver Oak College of Engineering and Technology. Copyright ? 2017 by Milap Bhanderi
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
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
?? 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
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 ?rst nine integers or 0 in each place and leXing each place value be a power of 10. Copyright ? 2017 by Milap Bhanderi
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
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
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 ¡Á 2 4 ) + (1 ¡Á 2 3 ) + (1 ¡Á 2 2 ) + (0 ¡Á 2 1 ) + (1 ¡Á 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
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
Copyright ? 2017 by Milap Bhanderi

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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 ?rst 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 ¡Á 2 4 ) + (1 ¡Á 2 3 ) + (1 ¡Á 2 2 ) + (0 ¡Á 2 1 ) + (1 ¡Á 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