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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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sampai jumpaminggu depan

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