02. Pertemuan 2
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2.1 Binary Coded Decimal2.1.1 BCD-to-Binary Conversion
2.1.2 Binary-to-BCD Conversion
2.1.3 Higher-Density BCD Encoding
2.1.4 Packed and Unpacked BCD Numbers
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Sistem Bilangan yang kita kenal saat iniadalah sistem angka desimal, yaitu bilangandengan bilangan dasar 10
Dalam setiap sistem bilangan senantiasamempunyai :
Bilangan dasar angka maksimum
Angka Absolut Jenis Lambang bilangan yang bernilaiberbedabeda (0,1,2,3,4,5,6,7,8,9)
Nilai Letak.
nilai yang tergantung pada posisi yaituperpangkatan dari bilangan dasarnya.
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Nama BilanganDasar Lambang Bilangan Yang muncul
Binary 2 0,1Ternary 3 0,1,2
Quarterrary 4 0,1,2,3
Quinary 5 0,1,2,3,4
Senary 6 0,1,2,3,4,5
Septenary 7 0,1,2,3,4,5,6
Octal 8 0,1,2,3,4,5,6,7
Novonary 9 0,1,2,3,4,5,6,7,8
Decimal 10 0,1,2,3,4,5,6,7,8,9
Uni decimal 11 0,1,2,3,4,5,6,7,8,9,ADuo decimal 12 0,1,2,3,4,5,6,7,8,9,A,B
Terdenary 13 0,1,2,3,4,5,6,7,8,9,A,B,C
Quarterdenary 14 0,1,2,3,4,5,6,7,8,9,A,B,C,D
Quidenary 15 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E
Hexa decimal 16 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F
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The binary coded decimal (BCD) is a type of binarycode used to represent a given decimal numberin an equivalent binary form.
As an example, the BCD equivalent of (23.15)10
is written as (0010 0011.0001 0101)BCD
2.1.1 BCD-to-Binary Conversion
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3/2=1 1
=0 0
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8/2=4 0
4/2=2 02/2=1 0
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A given BCD number can be converted into anequivalent binary number by first writing its decimalequivalent and then converting it into its binaryequivalent.
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BCD
8421 BCD
5 = 0101
2 = 0010
4 = 0100
Binary dari 524524/2=262 0
262/2=131 0
131/2=65
165/2=32 1
32/2=16 0
16/2=8 0
8/2-4 04/2=2 0
2/2=1 0
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A given binary number can be converted into anequivalent BCD number by first determining itsdecimal equivalent and then writing the correspondingBCD equivalent.
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1x23+0x22+0x21+0x20
8+ 0 + 0 + 0 (8)10
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In the regular BCD encoding of decimal numbers, thenumber of bits needed to represent a given decimal numberis always greater than the number of bits required forstraight binary encoding of the same. For example, a three-digit decimal number requires 12 bits for representation inconventional BCD format. However, since 210 > 103, ifthese three decimal digits are encoded together, only 10bits would be needed to do that. Two such encodingschemes are Chen-Ho encoding and the densely packeddecimal. The latter has the advantage that subsets of theencoding encode two digits in the optimal seven bits andone digit in four bits like regular BCD.
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In the case of packed BCD numbers, two BCD digits arestored in a single eight-bit register. Theprocess of combining two BCD digits so that they are stored
in one eight-bit register involves shiftingthe number in the upper register to the left 4 times and thenadding the numbers in the upper and lowerregisters..
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How many bits would be required to encode decimal
numbers 0 to 9999 in straight binary and BCD codes?What would be the BCD equivalent of decimal 27 in 16-bit representation?
Solution
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