NUMBER SYSTEM CONVERSIONS PDF A) Divide the Number (Decimal

Number System and Conversion

Decimal (Base 10). ? Binary (Base 2). ? Octal (Base 8). ? Hexadecimal (Base 16). ? The decimal system is the number system that we use everyday

NUMBER SYSTEM CONVERSIONS

A) Divide the Number (Decimal Number) by the base of target base system (in which you want to convert the number: Binary (2) octal (8) and Hexadecimal

A Step towards an Easy Interconversion of Various Number Systems

Section three describes all the conversion techniques. (both for integral and fraction part of the numbers) frequently used so far. Section four contains and

Lecture #2: Binary Hexadecimal

https://personal.utdallas.edu/~dodge/EE2310/lec2.pdf

kecs102.pdf

08-Apr-2019 To convert the fractional part of a decimal number to another number system with base value b repeatedly multiply the fractional part by the ...

3. Convert a number from one number system to another

The integer is the highest-order digit. 3. Repeat first two steps until fraction becomes zero. Example 1 Convert 2510 to binary number.

NUMBER SYSTEMS

Now if the number contains the fractional part we have to deal in a different way when converting the number from a different number system (i.e. binary

Convert 0.1011012 to base 10(or decimal) number Multiply each

Conversion of fractional numbers from one number system to another. •. Fractional Decimal to fractional Binary and Vice-Versa.

1 Number System (Lecture 1 and 2 supplement)

Due to the structure described above a fractional number expressed by decimal can be converted into a base “b” number by collecting the integer part from left

Number Systems and Radix Conversion

We'll return to fractional numbers in a bit. For now let's just consider integers. Exercise 1: What is (48A6)12 in decimal? (work it out in the space below1).

[PDF] Number System and Conversion

Many number systems are in use in digital technology The most common are : ? Decimal (Base 10) ? Binary (Base 2) ? Octal (Base 8)

[PDF] NUMBER SYSTEM CONVERSIONS - ipsgwaliororg

To convert Number system from Decimal Number System to Any Other Base is quite easy; you have to follow just two steps: A) Divide the Number (Decimal Number) by

[PDF] The Computer Number System - The University of Texas at Dallas

On either side of the hexadecimal point convert each hex digit to an equivalent 4-bit binary number and drop leading integral and trailing fractional zeroes

[PDF] NUMBER SYSTEM - 1st Semester Notes

For the conversion of the fractional binary number to hexadecimal number break the binary number in to the group of four points Convert each group of 4 bits

[PDF] NUMBER SYSTEMS

Now if the number contains the fractional part we have to deal in a different way when converting the number from a different number system (i e binary octal

[PDF] Number Systems

The conversion process of a decimal number into any number system can be done according to the following steps: 1- Separate the integer part and the fraction

[PDF] Number Conversions Dr Sarita Agarwal (Acharya Narendra Dev

Apart from the decimal number system there are binary number system octal number system and hexadecimal number system and so on Base (Radix) – In any

[PDF] Number System Conversion - Tutorialspoint

Shortcut method ? Hexadecimal to Binary Decimal to Other Base System Steps Step 1 ? Divide the decimal number to be converted by the value of the new

[PDF] 3 Convert a number from one number system to another

The integer is the highest-order digit 3 Repeat first two steps until fraction becomes zero Example 1 Convert 2510 to binary number

[PDF] Encoding Schemes and Number System

8 avr 2019 · In this section we will learn about conversion of numbers with a fractional part (A) Decimal Number with Fractional Part to another Number

What is the decimal for 0.1011 in binary?
Converting binary fraction to decimal
In this way 0.1011 in binary is 0.6875 in decimal.
How do you convert 0.5 to binary?
How do you represent 0.5 in binary? Multiply the 0.5 by 2 : 0.5 × 2 = 1.0 . Since the result is 1 , add 1 to the binary fraction: 0.1 . The remaining decimal part of the number is zero; thus, the representation is complete
How do you convert a fraction from base 10 to base 2?
Steps To Convert From Base 10 To Base 2-
1Multiply the given fraction (in base 10) with 2.2Write the real part and fractional part of the result so obtained separately.3Multiply the fractional part with 2.4Write the real part and fractional part of the result so obtained separately.
Conversions of Decimal Fractions to Octal Fractions – The conversion of decimal fraction to octal fraction is similar to decimal fraction to binary fraction. Here we multiply the fraction by 8 instead of 2. Example – Find the octal equivalent of (0.75)10. Number (to be recorded) 0.75 x 8 = 6.00 Thus (0.75)10 = (0.6)8.

NUMBER SYSTEM

Number systems are the technique to represent numbers in the computer system architecture, every value that you are saving or getting into/from computer memory has a defined number system. Computer architecture supports following number systems.

Binary number system

Octal number system

Decimal number system

Hexadecimal (hex) number system

BINARY NUMBER SYSTEM

A Binary number system has only two digits that are 0 and 1. Every number (value) represents with 0 and 1 in this number system. The base of binary number system is 2, because it has only two digits.

OCTAL NUMBER SYSTEM

Octal number system has only eight (8) digits from 0 to 7. Every number (value) represents with

0,1,2,3,4,5,6 and 7 in this number system. The base of octal number system is 8, because it has

only 8 digits.

DECIMAL NUMBER SYSTEM

Decimal number system has only ten (10) digits from 0 to 9. Every number (value) represents with 0,1,2,3,4,5,6, 7,8 and 9 in this number system. The base of decimal number system is 10, because it has only 10 digits.

HEXADECIMAL NUMBER SYSTEM

A Hexadecimal number system has sixteen (16) alphanumeric values from 0 to 9 and A to F. Every number (value) represents with 0,1,2,3,4,5,6, 7,8,9,A,B,C,D,E and F in this number system. The base of hexadecimal number system is 16, because it has 16 alphanumeric values. Here A is 10, B is 11, C is 12, D is 14, E is 15 and F is 16.

Number system Base(Radix) Used digits Example

Binary 2 0,1 (11110000)2

Octal 8 0,1,2,3,4,5,6,7 (360)8

Decimal 10 0,1,2,3,4,5,6,7,8,9 (240)10

Hexadecimal 16 0,1,2,3,4,5,6,7,8,9,

A,B,C,D,E,F (F0)16

CONVERSIONS

DECIMAL TO OTHER

1. DECIMAL TO BINARY

Decimal Number System to Other Base

To convert Number system from Decimal Number System to Any Other Base is quite easy; you have to follow just two steps: A) Divide the Number (Decimal Number) by the base of target base system (in which you want to convert the number: Binary (2), octal (8) and Hexadecimal (16)). B) Write the remainder from step 1 as a Least Signification Bit (LSB) to Step last as a Most

Significant Bit (MSB).

Decimal to Binary Conversion Result

Decimal Number is : (12345)10

Binary Number is

(11000000111001)2

2. DECIMAL TO OCTAL

Decimal to Octal Conversion Result

Decimal Number is : (12345)10

Octal Number is

(30071)8

3. DECIMAL TO HEXADECIMAL

Decimal to Hexadecimal Conversion Result

Example 1

Decimal Number is : (12345)10

Hexadecimal Number is

(3039)16

Example 2

Decimal Number is : (725)10

Hexadecimal Number is

(2D5)16

Convert

10, 11, 12, 13, 14, 15

to its equivalent...

A, B, C, D, E, F

BINARY TO OTHER

A) Multiply the digit with 2(with place value exponent). Eventually add all the multiplication becomes the Decimal number.

1. BINARY TO DECIMAL

2. BINARY TO OCTAL

An easy way to convert from binary to octal is to group binary digits into sets of three, starting with the least significant (rightmost) digits.

Binary: 11100101 = 11 100 101

011 100 101 Pad the most significant digits with zeros if

necessary to complete a group of three.

Then, look up each group in a table:

Binary: 000 001 010 011 100 101 110 111

Octal: 0 1 2 3 4 5 6 7

Binary = 011 100 101 Octal = 3 4 5 = 345 oct

3. BINARY TO HEXADECIMAL

An equally easy way to convert from binary to hexadecimal is to group binary digits into sets of four, starting with the least significant (rightmost) digits.

Binary: 11100101 = 1110 0101

Then, look up each group in a table:

Binary: 0000 0001 0010 0011 0100 0101 0110 0111

Hexadecimal: 0 1 2 3 4 5 6 7

Binary: 1000 1001 1010 1011 1100 1101 1110 1111

Hexadecimal: 8 9 A B C D E F

Binary = 1110 0101 Hexadecimal = E 5 = E5 hex

OCTAL TO OTHER

1. OCTAL TO BINARY

Converting from octal to binary is as easy as converting from binary to octal. Simply look up each octal digit to obtain the equivalent group of three binary digits.

Octal: 0 1 2 3 4 5 6 7

Binary: 000 001 010 011 100 101 110 111

Octal = 3 4 5 Binary = 011 100 101 = 011100101 binary

2. OCTAL TO HEXADECIMAL

When converting from octal to hexadecimal, it is often easier to first convert the octal number into binary and then from binary into hexadecimal. For example, to convert 345 octal into hex: (from the previous example)

Octal = 3 4 5

Binary = 011 100 101 = 011100101 binary

Drop any leading zeros or pad with leading zeros to get groups of four binary digits (bits):

Binary 011100101 = 1110 0101

Then, look up the groups in a table to convert to hexadecimal digits.

Binary: 0000 0001 0010 0011 0100 0101 0110 0111

Hexadecimal: 0 1 2 3 4 5 6 7

Binary: 1000 1001 1010 1011 1100 1101 1110 1111

Hexadecimal: 8 9 A B C D E F

Binary = 1110 0101

Hexadecimal = E 5 = E5 hex

Therefore, through a two-step conversion process, octal 345 equals binary 011100101 equals hexadecimal E5.

3. OCTAL TO DECIMAL

The conversion can also be performed in the conventional mathematical way, by showing each digit place as an increasing power of 8.

345 octal = (3 * 82) + (4 * 81) + (5 * 80) = (3 * 64) + (4 * 8) + (5 * 1) = 229 decimal

OR Converting octal to decimal can be done with repeated division.

1. Start the decimal result at 0.

2. Remove the most significant octal digit (leftmost) and add it to the result.

3. If all

4. Otherwise, multiply the result by 8.

5. Go to step 2.

Octal Digits Operation Decimal Result Operation Decimal Result

345 +3 3 × 8 24

45 +4 28 × 8 224

5 +5 229 done.

Ö (345)8 =(229)10

HEXADECIMAL TO OTHER

1. HEXADECIMAL TO BINARY

Converting from hexadecimal to binary is as easy as converting from binary to hexadecimal. Simply look up each hexadecimal digit to obtain the equivalent group of four binary digits.

Hexadecimal: 0 1 2 3 4 5 6 7

Binary: 0000 0001 0010 0011 0100 0101 0110 0111

Hexadecimal: 8 9 A B C D E F

Binary: 1000 1001 1010 1011 1100 1101 1110 1111

Hexadecimal = A 2 D E Binary = 1010 0010 1101 1110 = 1010001011011110 binary

2. HEXADECIMAL TO OCTAL

1's complement

The 1's complement of a number is found by changing all 1's to 0's and all 0's to 1's. This is called as taking complement or 1's complement. Example of 1's Complement is as follows.

Binary Addition

It is a key for binary subtraction, multiplication, division. There are four rules of binary addition.

In fourth case, a binary addition is creating a sum of (1 + 1 = 10) i.e. 0 is written in the given column and a carry of 1 over to the next column.

2's complement

The 2's complement of binary number is obtained by adding 1 to the Least Significant Bit (LSB) of 1's complement of the number.

2's complement = 1's complement + 1

Example of 2's Complement is as follows.

Rules of Binary Addition

0 + 0 = 0

0 + 1 = 1

1 + 0 = 1

1 + 1 = 0, and carry 1 to the next more significant bit

For example,

00011010 + 00001100 = 00100110 1 1 Carries

0 0 0 1 1 0 1 0 = 26(base 10)

+ 0 0 0 0 1 1 0 0 = 12(base 10)

0 0 1 0 0 1 1 0 = 38(base 10)

00010011 + 00111110 = 01010001 1 1 1 1 1 carries

0 0 0 1 0 0 1 1 = 19(base 10)

+ 0 0 1 1 1 1 1 0 = 62(base 10)

0 1 0 1 0 0 0 1 = 81(base 10)

Rules of Binary Multiplication

0 x 0 = 0

0 x 1 = 0

1 x 0 = 0

1 x 1 = 1, and no carry or borrow bits

For example,

00101001 × 00000110 = 11110110 0 0 1 0 1 0 0 1 = 41(base 10)

× 0 0 0 0 0 1 1 0

= 6(base 10)

0 0 0 0 0 0 0 0

0 0 1 0 1 0 0 1

0 0 1 1 1 1 0 1 1 0 = 246(base 10)

Binary Division

Binary division is the repeated process of subtraction, just as in decimal division.

For example,

00101010 ÷ 00000110 = 1 1 1 = 7(base 10)

00000111

1 1 0 ) 0 0 1 10 1 0 1 0 = 42(base 10)

- 1 1 0 = 6(base 10)

1 borrows

1 0 10 1

- 1 1 0

1 1 0

- 1 1 0 0

10000111 ÷ 00000101 =

00011011 1 1 0 1 1 = 27(base 10)

1 0 1 ) 1 0 0 10 0 1 1 1 = 135(base

10) - 1 0 1 = 5(base 10)

1 1 10

- 1 0 1 1 1 - 0

1 1 1

- 1 0 1

1 0 1

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[PDF] NUMBER SYSTEM CONVERSIONS A) Divide the Number (Decimal

What is the decimal for 0.1011 in binary?

How do you convert 0.5 to binary?

How do you convert a fraction from base 10 to base 2?

Steps To Convert From Base 10 To Base 2-

NUMBER SYSTEM

Binary number system

Octal number system

Decimal number system

Hexadecimal (hex) number system

BINARY NUMBER SYSTEM

OCTAL NUMBER SYSTEM

0,1,2,3,4,5,6 and 7 in this number system. The base of octal number system is 8, because it has

DECIMAL NUMBER SYSTEM

HEXADECIMAL NUMBER SYSTEM

Number system Base(Radix) Used digits Example

Binary 2 0,1 (11110000)2

Octal 8 0,1,2,3,4,5,6,7 (360)8

Decimal 10 0,1,2,3,4,5,6,7,8,9 (240)10

Hexadecimal 16 0,1,2,3,4,5,6,7,8,9,

A,B,C,D,E,F (F0)16

CONVERSIONS

DECIMAL TO OTHER

1. DECIMAL TO BINARY

Decimal Number System to Other Base

Significant Bit (MSB).

Decimal to Binary Conversion Result

Decimal Number is : (12345)10

Binary Number is

2. DECIMAL TO OCTAL

Decimal to Octal Conversion Result

Decimal Number is : (12345)10

Octal Number is

3. DECIMAL TO HEXADECIMAL

Decimal to Hexadecimal Conversion Result

Example 1

Decimal Number is : (12345)10

Hexadecimal Number is

Example 2

Decimal Number is : (725)10

Hexadecimal Number is

Convert

10, 11, 12, 13, 14, 15

A, B, C, D, E, F

BINARY TO OTHER

1. BINARY TO DECIMAL

2. BINARY TO OCTAL

Binary: 11100101 = 11 100 101

011 100 101 Pad the most significant digits with zeros if

Then, look up each group in a table:

Binary: 000 001 010 011 100 101 110 111

Octal: 0 1 2 3 4 5 6 7

Binary = 011 100 101 Octal = 3 4 5 = 345 oct

3. BINARY TO HEXADECIMAL

Binary: 11100101 = 1110 0101

Then, look up each group in a table:

Binary: 0000 0001 0010 0011 0100 0101 0110 0111

Hexadecimal: 0 1 2 3 4 5 6 7

Binary: 1000 1001 1010 1011 1100 1101 1110 1111

Hexadecimal: 8 9 A B C D E F

Binary = 1110 0101 Hexadecimal = E 5 = E5 hex

OCTAL TO OTHER

1. OCTAL TO BINARY

Octal: 0 1 2 3 4 5 6 7

Binary: 000 001 010 011 100 101 110 111

2. OCTAL TO HEXADECIMAL

Octal = 3 4 5

Binary = 011 100 101 = 011100101 binary

Binary 011100101 = 1110 0101

Binary: 0000 0001 0010 0011 0100 0101 0110 0111

Hexadecimal: 0 1 2 3 4 5 6 7

Binary: 1000 1001 1010 1011 1100 1101 1110 1111

Hexadecimal: 8 9 A B C D E F

Binary = 1110 0101

Hexadecimal = E 5 = E5 hex

3. OCTAL TO DECIMAL

345 octal = (3 * 82) + (4 * 81) + (5 * 80) = (3 * 64) + (4 * 8) + (5 * 1) = 229 decimal

1. Start the decimal result at 0.

2. Remove the most significant octal digit (leftmost) and add it to the result.

3. If all