Binary number

As an example of the decimal number 157 to:

157 (10) = (1 x 100) + (5 x 10) + (7 x 1)

Note! decimal number is often called a base 10. This is because perpangkatan 10 obtained from 100, 101, 102, ff.

Understanding binary concept and Decimal Numbers

Fundamental difference from the binary and decimal method is associated with the base. If a decimal-based 10 (X10) berpangkatkan 10x, then the binary number to base 2 (X2) using perpangkatan 2x. Sederhananya note the example below!

To Decimal:

14 (10) = (1 x 101) + (4 x 100)

= 10 + 4

= 14

To binary:

1110 (2) = (1 x 23) + (1 x 22) + (1 x 21) + (0 x 20)

= 8 + 4 + 2 + 0

= 14

General form of the binary and decimal numbers are:

Binary 1 1 1 1 1 1 1 1 11111111

Decimal 128 64 32 16 8 4 2 1 255

Rank 27 26 25 24 23 22 21 20 X1-7

Now we return to the example problem above! How did we get the decimal number 14 (10) into binary number 1110 (2)?

Let’s see more generally in the form!

Binary 0 0 0 0 1 1 1 0 00001110

Decimal 0 0 0 0 8 4 2 0 14

Rank 27 26 25 24 23 22 21 20 X1-7

Let’s browse through slowly!

• Firstly, we jumlahkan numbers in decimal, so a 14. you see the numbers that resulted in a number 14 is 8, 4, and 2!

• For the numbers that form the number 14 (see figures diarsir), marked binary “1”, the rest were given a “0”.

• So, if read from right, decimal number 14 will be 00001110 (sometimes read in 1110) in its binary digits.

Change binary to Decimal Numbers

Note the example!

1. 11001101 (2)

Binary 1 1 0 0 1 1 0 1 11001101

Decimal 128 64 0 0 8 4 0 1 205

Rank 27 26 25 24 23 22 21 20 X1-7

Note:

• Figures obtained from 205 decimal numbers in the Answer arsir (128 +64 +8 +4 +1)

• Each binary marked “1” will be counted, while the binary is marked “0” is not counted, alias “0” also.

2. 00111100 (2)

Binary 0 0 1 1 1 1 0 0 00111100

0 0 0 32 16 8 4 0 0 60

Rank 27 26 25 24 23 22 21 20 X1-7

Changing Decimal to binary number

To change the decimal numbers into binary numbers are used the method with the number 2 while the rest observe.

Note for example!

1. 205 (10)

205: 2 = 102 remainder 1

102: 2 = 51 remainder 0

51: 2 = 25 remainder 1

25: 2 = 12 remainder 1

12: 2 = 6 remainder 0

6: 2 = 3 remainder 0

3: 2 = 1 remainder 1

1 as the rest of the final “1”

Note:

To write down the notation binernya, reading is done from the bottom which means that 11,001,101 (2)

2. 60 (10)

60: 2 = 30 remainder 0

30: 2 = 15 remainder 0

15: 2 = 7 remainder 1

7: 2 = 3 remainder 1

3: 2 = 1 remainder 1

1 as the rest of the final “1”

Note:

Read from the bottom to be 111,100 (2) or is often written with 00,111,100 (2). Remember umumnnya form refers to 8 digits! 111100 if (this 6-digit) to 00111100 (this is 8 digits).

Binary arithmetic

In this section will discuss the Answer and binary. Binary multiplication is the repetition of the Answer and will also discuss the reduction of binary based on the idea or ideas complement.

Answer binary

Answer binary is not so much with the Answer decimal. Note the example Answer decimal between 167 and 235!

1 7 + 5 = 12, write “2” under and lift the “1” to the top!

167

235

—- +

402

As a decimal number, binary number also note in the same way. First is that the rules must be paired binary digits below:

0 + 0 = 0

0 + 1 = 1

1 + 1 = 0 and save 1

notes that as the number of the last two are:

1 + 1 + 1 = 1 with 1 save

With only the Answer-Answer the above, we can do Answer binary as shown below:

1111 “reserve 1” re-remember the rules above!

binary number 01011011 to 91

binary number 01001110 to 78

———— +

10101001 Number of 91 + 78 = 169

Please review the rules of binary digit pair mentioned above!

Sample Answer binary consisting of a 5!

11,101 the number 1)

10,110 the number 2)

1100 the number 3)

11,011 the number 4)

1001 the number 5)

——– +

for menjumlahkannya, we calculated based on the rules that apply, and for the calculation more easily done gradually!

What is the number of decimal

for the 1,2,3,4 and 5!

11,101 the number 1)

10,110 the number 2)

——- +

110011

1100 the number 3)

——- +

111111

11,011 the number 4)

——- +

011010

1001 the number 5)

——- +

End Number 1100011.

now try to specify how numbers 1,2,3,4 and 5! Whether the above calculation is correct?

Binary reduction

Decimal reduction of the number 73426 – 9185 will result in:

73426 see! Number 7 and number 4 was reduced with 1

9185 decimal digit subtrahend.

——— —

The reduction of 64,241 end.

General reduction in the form of:

0 – 0 = 0

1 – 0 = 0

1 – 1 = 0

0 – 1 = 1 with borrowed’1 ‘from the digits to the left!

For the reduction of binary can be done in the same way. Try to note the reduction in the following form:

1111011 decimal 123

101001 decimal 41

——— —

1010010 decimal 82

In the example above does not happen “the concept of borrowing.” Consider the following examples!

0 3-column to have a’0 ‘, have been borrowed!

111101 decimal 61

10010 decimal 18

———— —

Results 101,011 reduction last 43.

On this second issue we borrow’1 ‘from column 3, because no difference in columns 0-1 to-2. View Public shape!

7999 results loan

800046

397261

——— —

402705

For example reduction of binary numbers 110001 – 1010 results will be obtained as follows:

1100101

1010

———- —

100111

Supplement

One of the methods used in the reduction of the computer to be transformed by using the Answer minusradiks-one supplement or complement radiks. First, we complement in the decimal system, where complement-complement in a sequence is called the complement nine and ten complement (complement in the binary system with a single supplement and complement the two). Now the most important is this principle embed:

“Complement of nine decimal number obtained by subtract each digit to the decimal number 9, while the supplement is a supplement of ten nine-plus 1”

See examples of fact!

Decimal Numbers 123 651 914

Nine supplement 876 348 085

Ten supplement 877 349 086 plus 1!

Note the relationship between numbers and komplemennya is symmetrical. Thus, by considering the above example, 9 out of 123 supplement is made simple with the 876 number = 9 (1 +8 = 9, 2 +7 = 9, 3 +6 = 9)!

Meanwhile, 10 supplement 1 obtained by adding a supplement to the 9, it means that 876 +1 = 877!

Decimal reduction can be carried out with the Answer nine plus one supplement, or complement of ten Answer!

893 893 893

321 678 (komp. 9) 679 (komp. 10)

—- – —- + —- +

572 1571 1572

1

—- +

572 number 1 is removed!

Analogy that can be taken from the calculation above is a complement, one’s complement binary number obtained by way reduce each binary digit to the number 1, or with the language sederhananya change the 0 to 1 or change the 1 into 0 . While the supplement is a two plus one. Note the example.!

Binary number 110011 101010 011100

One complement 001100 010101 100011

Two complement 001101 010110 100100

Binary reduction 110001 – 1010 akan we study in the example below!

110001 110001 110001

001010 110101 110110

——— – ——— + ——— +

100111 100111 1100111

removed!

Theoretical reason why a supplement is done, attention can be explained with a speedometer car / motorcycle with four digits are read zero!

System octal and hex Decimal

Numbers is the octal base 8, while the number or hexadecimal often abbreviated into heks. This is based on the number 16. Because octal and heks is the designation of the two, they have a very close relationship. octal and hexadecimal principles related to the binary!

1. Change the number 63058 into the octal binary!

6 3 0 5 octal

110 011 000 101 binary

Note:

• Each digit octal ekivalens replaced with 3 bits (binary)

• For more details, see table below octal digits!

2. Change the heks 5D9316 into binary numbers!

heks binary

5 0101

D 1101

9 1001

3 0011

Note:

• So the number to binary heks 5D9316 is 0101110110010011

• For more details, see table below Hexadecimal Digits!

3. 1010100001101 change the binary into octal number!

001 010 100 001 101 binary

3 2 4 1 5 octal

Note:

• Group the binary number into 3-bit right from the start!

4. Change the binary number 101101011011001011 become heks!

0010 1101 0110 1100 1011 binary

2 D 6 CB heks

Table Digit octal

3-digit octal Ekivalens-Bit

0 000

1 001

2 010

3 011

4 100

5 101

6 110

7 111

Table Hexadecimal Digits

Decimal Digits Ekivalens 4-Bit

0 0000

1 0001

2 0010

3 0011

4 0100

5 0101

6 0110

7 0111

8 1000

9 1001

A (10) 1010

B (11) 1011

C (12) 1100

D (13) 1101

E (14) 1110

F (15) 1111

Binary number

As an example of the decimal number 157 to:

157 (10) = (1 x 100) + (5 x 10) + (7 x 1)

Note! decimal number is often called a base 10. This is because perpangkatan 10 obtained from 100, 101, 102, ff.

Understanding binary concept and Decimal Numbers

Fundamental difference from the binary and decimal method is associated with the base. If a decimal-based 10 (X10) berpangkatkan 10x, then the binary number to base 2 (X2) using perpangkatan 2x. Sederhananya note the example below!

To Decimal:

14 (10) = (1 x 101) + (4 x 100)

= 10 + 4

= 14

To binary:

1110 (2) = (1 x 23) + (1 x 22) + (1 x 21) + (0 x 20)

= 8 + 4 + 2 + 0

= 14

General form of the binary and decimal numbers are:

Binary 1 1 1 1 1 1 1 1 11111111

Decimal 128 64 32 16 8 4 2 1 255

Rank 27 26 25 24 23 22 21 20 X1-7

Now we return to the example problem above! How did we get the decimal number 14 (10) into binary number 1110 (2)?

Let’s see more generally in the form!

Binary 0 0 0 0 1 1 1 0 00001110

Decimal 0 0 0 0 8 4 2 0 14

Rank 27 26 25 24 23 22 21 20 X1-7

Let’s browse through slowly!

• Firstly, we jumlahkan numbers in decimal, so a 14. you see the numbers that resulted in a number 14 is 8, 4, and 2!

• For the numbers that form the number 14 (see figures diarsir), marked binary “1”, the rest were given a “0”.

• So, if read from right, decimal number 14 will be 00001110 (sometimes read in 1110) in its binary digits.

Change binary to Decimal Numbers

Note the example!

1. 11001101 (2)

Binary 1 1 0 0 1 1 0 1 11001101

Decimal 128 64 0 0 8 4 0 1 205

Rank 27 26 25 24 23 22 21 20 X1-7

Note:

• Figures obtained from 205 decimal numbers in the Answer arsir (128 +64 +8 +4 +1)

• Each binary marked “1” will be counted, while the binary is marked “0” is not counted, alias “0” also.

2. 00111100 (2)

Binary 0 0 1 1 1 1 0 0 00111100

0 0 0 32 16 8 4 0 0 60

Rank 27 26 25 24 23 22 21 20 X1-7

Changing Decimal to binary number

To change the decimal numbers into binary numbers are used the method with the number 2 while the rest observe.

Note for example!

1. 205 (10)

205: 2 = 102 remainder 1

102: 2 = 51 remainder 0

51: 2 = 25 remainder 1

25: 2 = 12 remainder 1

12: 2 = 6 remainder 0

6: 2 = 3 remainder 0

3: 2 = 1 remainder 1

À 1 as the remaining end of the “1”

Note:

To write down the notation binernya, reading is done from the bottom which means that 11,001,101 (2)

2. 60 (10)

60: 2 = 30 remainder 0

30: 2 = 15 remainder 0

15: 2 = 7 remainder 1

7: 2 = 3 remainder 1

3: 2 = 1 remainder 1

À 1 as the remaining end of the “1”

Note:

Read from the bottom to be 111,100 (2) or is often written with 00,111,100 (2). Remember umumnnya form refers to 8 digits! 111100 if (this 6-digit) to 00111100 (this is 8 digits).

Binary arithmetic

In this section will discuss the Answer and binary. Binary multiplication is the repetition of the Answer and will also discuss the reduction of binary based on the idea or ideas complement.

Answer binary

Answer binary is not so much with the Answer decimal. Note the example Answer decimal between 167 and 235!

1 7 + 5 = 12, write “2” under and lift the “1” to the top!

167

235

—- +

402

As a decimal number, binary number also note in the same way. First is that the rules must be paired binary digits below:

0 + 0 = 0

0 + 1 = 1

1 + 1 = 0 0 and save 1

notes that as the number of the last two are:

1 + 1 + 1 = 1 to save 1 à

With only the Answer-Answer the above, we can do Answer binary as shown below:

1 1111 0 “reserve 1” re-remember the rules above!

Binary number 01011011 to 91

Binary number 01001110 to 78

———— +

10101001 à Number of 91 + 78 = 169

Please review the rules of binary digit pair mentioned above!

Sample Answer binary consisting of a 5!

11,101 the number 1)

10,110 the number 2)

1100 the number 3)

11,011 the number 4)

1001 the number 5)

——– +

for menjumlahkannya, we calculated based on the rules that apply, and for the calculation more easily done gradually!

11,101 the number 1)

10,110 the number 2)

——- +

110011

1100 the number 3)

——- +

111111

11,011 the number 4)

——- +

011010

1001 the number 5)

——- +

1100011 à Number of End.

now try to specify how numbers 1,2,3,4 and 5! Whether the above calculation is correct?

Binary reduction

Decimal reduction of the number 73426 – 9185 will result in:

73426 à see! Number 7 and number 4 was reduced with 1

9185 à subtrahend digit decimal.

——— —

Results 64241 à final reduction.

General reduction in the form of:

0 – 0 = 0

1 – 0 = 0

1 – 1 = 0

0 – 1 = 1 with a borrow’1 ‘from the digits to the left!

For the reduction of binary can be done in the same way. Try to note the reduction in the following form:

1111011 à 123 decimal

101,001 decimal à 41

——— —

1010010 à 82 decimal

In the example above does not happen “the concept of borrowing.” Consider the following examples!

0 à 3-column to have a’0 ‘, have been borrowed!

111,101 decimal à 61

10,010 decimal à 18

———— —

À reduction of 101,011 Results end 43.

On this second issue we borrow’1 ‘from column 3, because no difference in columns 0-1 to-2. View Public shape!

7999 à result of loan

800046

397261

——— —

402705

For example reduction of binary numbers 110001 – 1010 results will be obtained as follows:

1100101

1010

———- —

100111

Supplement

One of the methods used in the reduction of the computer to be transformed by using the Answer minusradiks-one supplement or complement radiks. First, we complement in the decimal system, where complement-complement in a sequence is called the complement nine and ten complement (complement in the binary system with a single supplement and complement the two). Now the most important is this principle embed:

“Complement of nine decimal number obtained by subtract each digit to the decimal number 9, while the supplement is a supplement of ten nine-plus 1”

See examples of fact!

Decimal Numbers 123 651 914

Nine supplement 876 348 085

Ten supplement 877 349 086 plus the 1!

Note the relationship between numbers and komplemennya is symmetrical. Thus, by considering the above example, 9 out of 123 supplement is made simple with the 876 number = 9 (1 +8 = 9, 2 +7 = 9, 3 +6 = 9)!

Meanwhile, 10 supplement 1 obtained by adding a supplement to the 9, it means that 876 +1 = 877!

Decimal reduction can be carried out with the Answer nine plus one supplement, or complement of ten Answer!

893 893 893

321 678 (komp. 9) 679 (komp. 10)

—- – —- + —- +

572 1571 1572

1

—- +

572 number 1 is removed!

Analogy that can be taken from the calculation above is a complement, one’s complement binary number obtained by way reduce each binary digit to the number 1, or with the language sederhananya change the 0 to 1 or change the 1 into 0 . While the supplement is a two plus one. Note the example.!

Binary number 110011 101010 011100

One complement 001100 010101 100011

Two complement 001101 010110 100100

Binary reduction 110001 – 1010 akan we study in the example below!

110001 110001 110001

001010 110101 110110

——— – ——— + ——— +

100111 100111 1100111

removed!

Theoretical reason why a supplement is done, attention can be explained with a speedometer car / motorcycle with four digits are read zero!

System octal and hex Decimal

Numbers is the octal base 8, while the number or hexadecimal often abbreviated into heks. This is based on the number 16. Because octal and heks is the designation of the two, they have a very close relationship. octal and hexadecimal principles related to the binary!

1. Change the number 63058 into the octal binary!

6 3 0 5 à octal

110 011 000 101 à binary

Note:

• Each digit octal ekivalens replaced with 3 bits (binary)

• For more details, see table below octal digits!

2. Change the heks 5D9316 into binary numbers!

heks binary

5 0101

D 1101

9 1001

3 0011

Note:

• So the number to binary heks 5D9316 is 0101110110010011

• For more details, see table below Hexadecimal Digits!

3. 1010100001101 change the binary into octal number!

001 010 100 001 101 à binary

3 2 4 1 5 à octal

Note:

• Group the binary number into 3-bit right from the start!

4. Change the binary number 101101011011001011 become heks!

0010 1101 0110 1100 1011 à binary

2 D 6 CB à heks

Table Digit octal

3-digit octal Ekivalens-Bit

0 000

1 001

2 010

3 011

4 100

5 101

6 110

7 111

Table Hexadecimal Digits

Decimal Digits Ekivalens 4-Bit

0 0000

1 0001

2 0010

3 0011

4 0100

5 0101

6 0110

7 0111

8 1000

9 1001

A (10) 1010

B (11) 1011

C (12) 1100

D (13) 1101

E (14) 1110

F (15) 1111

1. Nyatakanlah-number decimal number system in the following numbers:

a. Binary, b. Octal, c. Hexadecimal.

5 11 38 1075 3500 1 0.35 3,625 4.33

2. Tentukanlah kompelemen 1 and kompelemen 2 of the following binary numbers:

1010 1101 11010100 1001001

3. Tentukanlah kompelemen 9 and kompelemen decimal number 10 of the following:

21 139 2400 9101

4. Tentukanlah kompelemen 7 and kompelemen 8 of the octal number of the following:

21 137 320 161

5. Tentukanlah kompelemen 15, and 16 of the kompelemen Hexadecimal:

BAC B3F 120 1A1

6. With 8-bit word length and bit the left states a sign, and 0 = positive 1 = negative, nyatakanlah number-decimal numbers in binary with the following use kompelemen 1 and kompelemen 2:

7 -11 -27

7. In a system using 16 bit word size, price tentukanlah-decimal number from the following:

Binary: 0100 1101 1100 1000; 1011 0100 1010 0101

Octal: 73; 201; 172

Hexadecimal: 6B; A5; 7C

8. Answer with the operation, conducted a reduction in the following:

Decimal: 125 – 32; 15 – 72

Binary: 1001 – 1000; 1001 – 1110

(8-bit word length)