Tugas 3 [Dwi Nita Maulida] Sistem Bilangan"
- Desimal 0-9
- Biner 0-1
- oktal 0-7
- Hexadesimal 0-f
- Suatu Bilangan biner merupakan cara lain untuk melambangkan kuantitas, dimana 1 (high) dan 0 (low)
- Sistem bilangan biner mempunyai nilai basis 2 dengan nilai setiap posisi dibagi dengan faktor 2
- Metode Sum-Of-Weight
- pengulangan pembagian dengan metode bilangan 2
- konversi fraksi desimal ke biner
Binary Arithmetic
- Binary arithmetic is essential in all digital computers and in many other types of digital systems
- Addition, subtraction, multiplication, and division
Binary Division
- The 1's and 2's complements of binary numbers are very important because they permit the representation of negative numbers
- The method of 2's compliment arithmetic is commonly used in computers to handle negative numbers
- Start at the right with the LSB and write the bits as they are up and including the first 1
- take the 1's complements of the remaining bits
Digital systems, such as the computer, must be able to
handle both positive and negative numbers. A signed binary number consists of
both sign and magnitude information. The sign indicates whether a number is
positive or negative and the magnitude is the value of the number. There three
forms in which signed integer (whole) numbers can be represented in binary:
Sign-Magnitude
1’s Complement
2’s Complement
The sign Bit
The left-most bit in a signed binary number is the which tells you whether the number is positive or negetive
0 = positive number and 1= negative number
sign- magnitude form
When a signed binary number is represented in
sign-magnitude, the left-most bit is the sign bit and the remaining bits are
the magnitude bits. The magnitude bits are in true (uncomplemented) binary for
both positive and negative numbers.
Decimal number, +25 is expressed as an 8-bit signed binary
number using sign-magnitude form as: 00011001
1's Complement form
Positive numbers in 1’s complement form are represented the
same way as the positive sign-magnitude numbers. Negative numbers, however, are
the 1’s complements of the corresponding positive numbers. Example: The decimal
number -25 is expressed as the 1’s complement of +25 (00011001) as (11100110)
2's complement form
in the 2's complement form, a negative number is the 2's complement of the corresponding positive number
The Decimal value of signed numbers
sign magnitude : Decimal Value of positive and negative numbers in the sign-magnitude form are determined by summing the weights in all the magnitude bit positions where there are 1s and ignoring those positions where there are zeros.
1's complement : Decimal values of negative numbers are determined by assigning a negative value to the weight of the sign bit, summing all the weight where there are 1s and adding 1 to the result
2's complement: The weight of the sign bit in a negative number is given a negative value
Arithmetic Operation With Signed Number
In this section we will learn how signed numbers are added,
subtracted, multiplied and divided. This section will cover only on the 2’s
complement arithmetic, because, it widely used in computers and
microprocessor-based system .
Addition
both number positive : the sum is positive and is therefore in true binary
positive number with magnitude larger than negative number: the final carry is discarderded. the sum is positive and is therefore in true binary
Negative Number with magnitude large than positive number : The sum is Negative and is Therefore in 2's complement form
both number negative : the final carry is discarded. the sum is negative and is therefore in 2's complement form
Subtraction
To subtract two signed
numbers, take the 2’s Complement of the subtrahend and ADD. Discard any
final carry bit
Multiplication
The numbers in a multiplication are the multiplicand, the
multiplier and the product. Direct
Addition and Partial Products are two basic methods for performing
multiplication using addition.
Division
The division operation in computers is accomplished using
subtraction. Since subtraction is done with an adder, division can also be
accomplished with an adder. The result of a division is called the quotient.
Hexadecimal Numbers
- Most digital systems deal with groups of bits in even powers of 2 such as 8, 16, 32, and 64 bits.
- Hexadecimal uses groups of 4 bits.
- Base 16
16 possible symbols
0-9 and A-F
- Allows for convenient handling of long binary strings.
- convert from hex to decimal by multipliying each hex digit by its positional weight.
- Convert from decimal to hex by using the repeated division
method used for decimal to binary and decimal to octal conversion.
- Divide the decimal number by 16
- The first remainder is the LSB and the last is the MSB.
Note, when done on a calculator a decimal remainder can be multiplied by 16 to get the result. If the remainder is greater than 9, the letters A through F are used
- Hexadecimal is useful for representing long strings of bits.
- Understanding the conversion process and memorizing the 4
bit patterns for each hexadecimal digit will prove valuable later
BCD
- Binary Coded Decimal (BCD) is another way to present decimal
numbers in binary form.
- BCD is widely used and combines features of both decimal and
binary systems.
- Each digit is converted to a binary equivalent.
- To convert the number 87410 to BCD:
8 7 4
1000
0111 0100 =
100001110100BCD
- Each decimal digit is represented using 4 bits.
- Each 4-bit group can never be greater than 9.
- Reverse the process to convert BCD to decimal
- BCD is not a number system.
- BCD is a decimal number with each
digit encoded to its binary equivalent.
- A BCD number is not the same as a
straight binary number.
- The primary advantage of BCD is the
relative ease of converting to and from decimal.
- ASCII – American Standard Code for
Information Interchange.
a. Seven bit code: 27 = 128 possible
code groups
b. Table 2-4 lists the standard ASCII
codes
c. Examples of use are: to transfer information between computers,
between computers and printers, and for internal storage.
sumber : https://onlinelearning.uhamka.ac.id
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