To express: A binary number into a hexadecimal number.

Question

Want to see more full solutions like this?

Answer 1

Question

Chapter 85, Problem 18A

To determine

To express:

A binary number into a hexadecimal number.

Expert Solution & Answer

Answer to Problem 18A

Hexadecimal number is 749.A44₁₆.

Explanation of Solution

Given information:

A binary number 11101001001.1010010001₂.

Calculation:

Binary number system uses the number 2 as its base. Therefore, it has 2 symbols: The numbers are 0 and 1.

And a hexadecimal number system uses the number 16 as its base i.e. it has 16 symbols, hexadecimal digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F.

Binary numbers are represented as from hexadecimal number

Binary	0000	0001	0010	0011	0100	0101	0110	0111
Decimal	0	1	2	3	4	5	6	7
Hexadecimal	0	1	2	3	4	5	6	7

Binary	1000	1001	1010	1011	1100	1101	1110	1111
Decimal	8	9	10	11	12	13	14	15
Hexadecimal	8	9	A	B	C	D	E	F

Each hexadecimal digit consists of 4 binary digits.

For example, hexadecimal number 9 is equal to binary number 1001.

For converting integer part of binary number into hexadecimal number, write down the binary number and represent four binary digits from right by its hexadecimal digit from the table.

Then combine all the digits together.

For converting fractional part of binary number into hexadecimal number, write down the binary number and represent four binary digits from left by its hexadecimal digit from the table.

Then combine all the digits together.

Finally, hexadecimal number is combination of both integer and fractional part.

Hexadecimal digits are equal to the summation of 2ⁿ where n = 0, 1, 2 and 3 (position from right).

For example, 9 = 2³+2⁰. In this example, 2¹ and 2²are not there. So, at position 1 and 2, binary digit is zero, and at position 0 and 3, binary digit is one. Therefore, hexadecimal of binary 1001 is

Mathematics For Machine Technology, Chapter 85, Problem 18A

The hexadecimal number is equal to the summation of binary digits d_n × 2ⁿ

Divide the binary number into block of four digits. If four digits are not there, then add additional zero in binary number. For example, 11 is written as 0011 and .11 is written as .1100.

Hexadecimal of binary number 1100100101001011.1001001001₂ is (Starting from right for integer part and starting from left for fractional part)

$binary number= 0111 0100 1001 . 1010 0100 0100 →six hexadecimal digits are exist$

$first hexadecimal digit=0× 2 3 +1× 2 2 +1× 2 1 +1× 2 0$

$first hexadecimal digit=0×8+1×4+1×2+1×1$

$first hexadecimal digit=0+4+2+1$

$first hexadecimal digit=7$

$second hexadecimal digit=0× 2 3 +1× 2 2 +0× 2 1 +0× 2 0$

$second hexadecimal digit=0×8+1×4+0×2+0×1$

$second hexadecimal digit=0+4+0+0$

$second hexadecimal digit=4$

$third hexadecimal digit=1× 2 3 +0× 2 2 +0× 2 1 +1× 2 0$

$third hexadecimal digit=1×8+0×4+0×2+1×1$

$third hexadecimal digit=8+0+0+1$

$third hexadecimal digit=9$

$fourth hexadecimal digit=1× 2 3 +0× 2 2 +1× 2 1 +0× 2 0$

$fourth hexadecimal digit=1×8+0×4+1×2+0×1$

$fourth hexadecimal digit=8+0+2+0$

$fourth hexadecimal digit=10=A$

$fifth hexadecimal digit=0× 2 3 +1× 2 2 +0× 2 1 +0× 2 0$

$fifth hexadecimal digit=0×8+1×4+0×2+0×1$

$fifth hexadecimal digit=0+4+0+0$

$fifth hexadecimal digit=4$

$sixth hexadecimal digit=0× 2 3 +1× 2 2 +0× 2 1 +0× 2 0$

$sixth hexadecimal digit=0×8+1×4+0×2+0×1$

$sixth hexadecimal digit=0+4+0+0$

$sixth hexadecimal digit=4$

$So hexadecimal of given binary number = 749.A 44 16$

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Students have asked these similar questions

1. Give a subset that satisfies all the following properties simultaneously: Subspace Convex set Affine set Balanced set Symmetric set Hyperspace Hyperplane 2. Give a subset that satisfies some of the conditions mentioned in (1) but not all, with examples. 3. Provide a mathematical example (not just an explanation) of the union of two balanced sets that is not balanced. 4. What is the precise mathematical condition for the union of two hyperspaces to also be a hyperspace? Provide a proof. edited 9:11

2. You manage a chemical company with 2 warehouses. The following quantities of Important Chemical A have arrived from an international supplier at 3 different ports: Chemical Available (L) Port 1. 400 Port 2 110 Port 3 100 The following amounts of Important Chemical A are required at your warehouses: Warehouse 1 Warehouse 2 Chemical Required (L) 380 230 The cost in £ to ship 1L of chemical from each port to each warehouse is as follows: Warehouse 1 Warehouse 2 Port 1 £10 £45 Port 2 £20 £28 Port 3 £13 £11 (a) You want to know how to send these shipments as cheaply as possible. For- mulate this as a linear program (you do not need to formulate it in standard inequality form). (b) Suppose now that all is as in the previous question but that only 320L of Important Chemical A are now required at Warehouse 1. Any excess chemical can be transported to either Warehouse 1 or 2 for storage, in which case the company must pay only the relevant transportation costs, or can be disposed of at the…

choose true options in these from given question a) always full and always crossing. b) always full and sometimes crossing. c) always full and never crossing. d) sometimes full and always crossing. e) sometimes full and sometimes crossing. f) sometimes full and never crossing. g) never full and always crossing. h) never full and sometimes crossing. i) never full and never crossing.

Answer 2

Question

Chapter 85, Problem 18A

To determine

To express:

A binary number into a hexadecimal number.

Expert Solution & Answer

Answer to Problem 18A

Hexadecimal number is 749.A44₁₆.

Explanation of Solution

Given information:

A binary number 11101001001.1010010001₂.

Calculation:

Binary number system uses the number 2 as its base. Therefore, it has 2 symbols: The numbers are 0 and 1.

And a hexadecimal number system uses the number 16 as its base i.e. it has 16 symbols, hexadecimal digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F.

Binary numbers are represented as from hexadecimal number

Binary	0000	0001	0010	0011	0100	0101	0110	0111
Decimal	0	1	2	3	4	5	6	7
Hexadecimal	0	1	2	3	4	5	6	7

Binary	1000	1001	1010	1011	1100	1101	1110	1111
Decimal	8	9	10	11	12	13	14	15
Hexadecimal	8	9	A	B	C	D	E	F

Each hexadecimal digit consists of 4 binary digits.

For example, hexadecimal number 9 is equal to binary number 1001.

For converting integer part of binary number into hexadecimal number, write down the binary number and represent four binary digits from right by its hexadecimal digit from the table.

Then combine all the digits together.

For converting fractional part of binary number into hexadecimal number, write down the binary number and represent four binary digits from left by its hexadecimal digit from the table.

Then combine all the digits together.

Finally, hexadecimal number is combination of both integer and fractional part.

Hexadecimal digits are equal to the summation of 2ⁿ where n = 0, 1, 2 and 3 (position from right).

For example, 9 = 2³+2⁰. In this example, 2¹ and 2²are not there. So, at position 1 and 2, binary digit is zero, and at position 0 and 3, binary digit is one. Therefore, hexadecimal of binary 1001 is

Mathematics For Machine Technology, Chapter 85, Problem 18A

The hexadecimal number is equal to the summation of binary digits d_n × 2ⁿ

Divide the binary number into block of four digits. If four digits are not there, then add additional zero in binary number. For example, 11 is written as 0011 and .11 is written as .1100.

Hexadecimal of binary number 1100100101001011.1001001001₂ is (Starting from right for integer part and starting from left for fractional part)

$binary number= 0111 0100 1001 . 1010 0100 0100 →six hexadecimal digits are exist$

$first hexadecimal digit=0× 2 3 +1× 2 2 +1× 2 1 +1× 2 0$

$first hexadecimal digit=0×8+1×4+1×2+1×1$

$first hexadecimal digit=0+4+2+1$

$first hexadecimal digit=7$

$second hexadecimal digit=0× 2 3 +1× 2 2 +0× 2 1 +0× 2 0$

$second hexadecimal digit=0×8+1×4+0×2+0×1$

$second hexadecimal digit=0+4+0+0$

$second hexadecimal digit=4$

$third hexadecimal digit=1× 2 3 +0× 2 2 +0× 2 1 +1× 2 0$

$third hexadecimal digit=1×8+0×4+0×2+1×1$

$third hexadecimal digit=8+0+0+1$

$third hexadecimal digit=9$

$fourth hexadecimal digit=1× 2 3 +0× 2 2 +1× 2 1 +0× 2 0$

$fourth hexadecimal digit=1×8+0×4+1×2+0×1$

$fourth hexadecimal digit=8+0+2+0$

$fourth hexadecimal digit=10=A$

$fifth hexadecimal digit=0× 2 3 +1× 2 2 +0× 2 1 +0× 2 0$

$fifth hexadecimal digit=0×8+1×4+0×2+0×1$

$fifth hexadecimal digit=0+4+0+0$

$fifth hexadecimal digit=4$

$sixth hexadecimal digit=0× 2 3 +1× 2 2 +0× 2 1 +0× 2 0$

$sixth hexadecimal digit=0×8+1×4+0×2+0×1$

$sixth hexadecimal digit=0+4+0+0$

$sixth hexadecimal digit=4$

$So hexadecimal of given binary number = 749.A 44 16$

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Chapter 85, Problem 18A

To determine

To express:

A binary number into a hexadecimal number.

Expert Solution & Answer

Answer to Problem 18A

Hexadecimal number is 749.A44₁₆.

Explanation of Solution

Given information:

A binary number 11101001001.1010010001₂.

Calculation:

Binary number system uses the number 2 as its base. Therefore, it has 2 symbols: The numbers are 0 and 1.

And a hexadecimal number system uses the number 16 as its base i.e. it has 16 symbols, hexadecimal digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F.

Binary numbers are represented as from hexadecimal number

Binary	0000	0001	0010	0011	0100	0101	0110	0111
Decimal	0	1	2	3	4	5	6	7
Hexadecimal	0	1	2	3	4	5	6	7

Binary	1000	1001	1010	1011	1100	1101	1110	1111
Decimal	8	9	10	11	12	13	14	15
Hexadecimal	8	9	A	B	C	D	E	F

Each hexadecimal digit consists of 4 binary digits.

For example, hexadecimal number 9 is equal to binary number 1001.

For converting integer part of binary number into hexadecimal number, write down the binary number and represent four binary digits from right by its hexadecimal digit from the table.

Then combine all the digits together.

For converting fractional part of binary number into hexadecimal number, write down the binary number and represent four binary digits from left by its hexadecimal digit from the table.

Then combine all the digits together.

Finally, hexadecimal number is combination of both integer and fractional part.

Hexadecimal digits are equal to the summation of 2ⁿ where n = 0, 1, 2 and 3 (position from right).

For example, 9 = 2³+2⁰. In this example, 2¹ and 2²are not there. So, at position 1 and 2, binary digit is zero, and at position 0 and 3, binary digit is one. Therefore, hexadecimal of binary 1001 is

Mathematics For Machine Technology, Chapter 85, Problem 18A

The hexadecimal number is equal to the summation of binary digits d_n × 2ⁿ

Divide the binary number into block of four digits. If four digits are not there, then add additional zero in binary number. For example, 11 is written as 0011 and .11 is written as .1100.

Hexadecimal of binary number 1100100101001011.1001001001₂ is (Starting from right for integer part and starting from left for fractional part)

$binary number= 0111 0100 1001 . 1010 0100 0100 →six hexadecimal digits are exist$

$first hexadecimal digit=0× 2 3 +1× 2 2 +1× 2 1 +1× 2 0$

$first hexadecimal digit=0×8+1×4+1×2+1×1$

$first hexadecimal digit=0+4+2+1$

$first hexadecimal digit=7$

$second hexadecimal digit=0× 2 3 +1× 2 2 +0× 2 1 +0× 2 0$

$second hexadecimal digit=0×8+1×4+0×2+0×1$

$second hexadecimal digit=0+4+0+0$

$second hexadecimal digit=4$

$third hexadecimal digit=1× 2 3 +0× 2 2 +0× 2 1 +1× 2 0$

$third hexadecimal digit=1×8+0×4+0×2+1×1$

$third hexadecimal digit=8+0+0+1$

$third hexadecimal digit=9$

$fourth hexadecimal digit=1× 2 3 +0× 2 2 +1× 2 1 +0× 2 0$

$fourth hexadecimal digit=1×8+0×4+1×2+0×1$

$fourth hexadecimal digit=8+0+2+0$

$fourth hexadecimal digit=10=A$

$fifth hexadecimal digit=0× 2 3 +1× 2 2 +0× 2 1 +0× 2 0$

$fifth hexadecimal digit=0×8+1×4+0×2+0×1$

$fifth hexadecimal digit=0+4+0+0$

$fifth hexadecimal digit=4$

$sixth hexadecimal digit=0× 2 3 +1× 2 2 +0× 2 1 +0× 2 0$

$sixth hexadecimal digit=0×8+1×4+0×2+0×1$

$sixth hexadecimal digit=0+4+0+0$

$sixth hexadecimal digit=4$

$So hexadecimal of given binary number = 749.A 44 16$

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 85, Problem 18A

To determine

To express:

A binary number into a hexadecimal number.

Expert Solution & Answer

Answer to Problem 18A

Hexadecimal number is 749.A44₁₆.

Explanation of Solution

Given information:

A binary number 11101001001.1010010001₂.

Calculation:

Binary number system uses the number 2 as its base. Therefore, it has 2 symbols: The numbers are 0 and 1.

And a hexadecimal number system uses the number 16 as its base i.e. it has 16 symbols, hexadecimal digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F.

Binary numbers are represented as from hexadecimal number

Binary	0000	0001	0010	0011	0100	0101	0110	0111
Decimal	0	1	2	3	4	5	6	7
Hexadecimal	0	1	2	3	4	5	6	7

Binary	1000	1001	1010	1011	1100	1101	1110	1111
Decimal	8	9	10	11	12	13	14	15
Hexadecimal	8	9	A	B	C	D	E	F

Each hexadecimal digit consists of 4 binary digits.

For example, hexadecimal number 9 is equal to binary number 1001.

For converting integer part of binary number into hexadecimal number, write down the binary number and represent four binary digits from right by its hexadecimal digit from the table.

Then combine all the digits together.

For converting fractional part of binary number into hexadecimal number, write down the binary number and represent four binary digits from left by its hexadecimal digit from the table.

Then combine all the digits together.

Finally, hexadecimal number is combination of both integer and fractional part.

Hexadecimal digits are equal to the summation of 2ⁿ where n = 0, 1, 2 and 3 (position from right).

For example, 9 = 2³+2⁰. In this example, 2¹ and 2²are not there. So, at position 1 and 2, binary digit is zero, and at position 0 and 3, binary digit is one. Therefore, hexadecimal of binary 1001 is

Mathematics For Machine Technology, Chapter 85, Problem 18A

The hexadecimal number is equal to the summation of binary digits d_n × 2ⁿ

Divide the binary number into block of four digits. If four digits are not there, then add additional zero in binary number. For example, 11 is written as 0011 and .11 is written as .1100.

Hexadecimal of binary number 1100100101001011.1001001001₂ is (Starting from right for integer part and starting from left for fractional part)

$binary number= 0111 0100 1001 . 1010 0100 0100 →six hexadecimal digits are exist$

$first hexadecimal digit=0× 2 3 +1× 2 2 +1× 2 1 +1× 2 0$

$first hexadecimal digit=0×8+1×4+1×2+1×1$

$first hexadecimal digit=0+4+2+1$

$first hexadecimal digit=7$

$second hexadecimal digit=0× 2 3 +1× 2 2 +0× 2 1 +0× 2 0$

$second hexadecimal digit=0×8+1×4+0×2+0×1$

$second hexadecimal digit=0+4+0+0$

$second hexadecimal digit=4$

$third hexadecimal digit=1× 2 3 +0× 2 2 +0× 2 1 +1× 2 0$

$third hexadecimal digit=1×8+0×4+0×2+1×1$

$third hexadecimal digit=8+0+0+1$

$third hexadecimal digit=9$

$fourth hexadecimal digit=1× 2 3 +0× 2 2 +1× 2 1 +0× 2 0$

$fourth hexadecimal digit=1×8+0×4+1×2+0×1$

$fourth hexadecimal digit=8+0+2+0$

$fourth hexadecimal digit=10=A$

$fifth hexadecimal digit=0× 2 3 +1× 2 2 +0× 2 1 +0× 2 0$

$fifth hexadecimal digit=0×8+1×4+0×2+0×1$

$fifth hexadecimal digit=0+4+0+0$

$fifth hexadecimal digit=4$

$sixth hexadecimal digit=0× 2 3 +1× 2 2 +0× 2 1 +0× 2 0$

$sixth hexadecimal digit=0×8+1×4+0×2+0×1$

$sixth hexadecimal digit=0+4+0+0$

$sixth hexadecimal digit=4$

$So hexadecimal of given binary number = 749.A 44 16$

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 85, Problem 18A

To determine

To express:

A binary number into a hexadecimal number.

Expert Solution & Answer

Answer to Problem 18A

Hexadecimal number is 749.A44₁₆.

Explanation of Solution

Given information:

A binary number 11101001001.1010010001₂.

Calculation:

Binary number system uses the number 2 as its base. Therefore, it has 2 symbols: The numbers are 0 and 1.

And a hexadecimal number system uses the number 16 as its base i.e. it has 16 symbols, hexadecimal digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F.

Binary numbers are represented as from hexadecimal number

Binary	0000	0001	0010	0011	0100	0101	0110	0111
Decimal	0	1	2	3	4	5	6	7
Hexadecimal	0	1	2	3	4	5	6	7

Binary	1000	1001	1010	1011	1100	1101	1110	1111
Decimal	8	9	10	11	12	13	14	15
Hexadecimal	8	9	A	B	C	D	E	F

Each hexadecimal digit consists of 4 binary digits.

For example, hexadecimal number 9 is equal to binary number 1001.

For converting integer part of binary number into hexadecimal number, write down the binary number and represent four binary digits from right by its hexadecimal digit from the table.

Then combine all the digits together.

For converting fractional part of binary number into hexadecimal number, write down the binary number and represent four binary digits from left by its hexadecimal digit from the table.

Then combine all the digits together.

Finally, hexadecimal number is combination of both integer and fractional part.

Hexadecimal digits are equal to the summation of 2ⁿ where n = 0, 1, 2 and 3 (position from right).

For example, 9 = 2³+2⁰. In this example, 2¹ and 2²are not there. So, at position 1 and 2, binary digit is zero, and at position 0 and 3, binary digit is one. Therefore, hexadecimal of binary 1001 is

Mathematics For Machine Technology, Chapter 85, Problem 18A

The hexadecimal number is equal to the summation of binary digits d_n × 2ⁿ

Divide the binary number into block of four digits. If four digits are not there, then add additional zero in binary number. For example, 11 is written as 0011 and .11 is written as .1100.

Hexadecimal of binary number 1100100101001011.1001001001₂ is (Starting from right for integer part and starting from left for fractional part)

$binary number= 0111 0100 1001 . 1010 0100 0100 →six hexadecimal digits are exist$

$first hexadecimal digit=0× 2 3 +1× 2 2 +1× 2 1 +1× 2 0$

$first hexadecimal digit=0×8+1×4+1×2+1×1$

$first hexadecimal digit=0+4+2+1$

$first hexadecimal digit=7$

$second hexadecimal digit=0× 2 3 +1× 2 2 +0× 2 1 +0× 2 0$

$second hexadecimal digit=0×8+1×4+0×2+0×1$

$second hexadecimal digit=0+4+0+0$

$second hexadecimal digit=4$

$third hexadecimal digit=1× 2 3 +0× 2 2 +0× 2 1 +1× 2 0$

$third hexadecimal digit=1×8+0×4+0×2+1×1$

$third hexadecimal digit=8+0+0+1$

$third hexadecimal digit=9$

$fourth hexadecimal digit=1× 2 3 +0× 2 2 +1× 2 1 +0× 2 0$

$fourth hexadecimal digit=1×8+0×4+1×2+0×1$

$fourth hexadecimal digit=8+0+2+0$

$fourth hexadecimal digit=10=A$

$fifth hexadecimal digit=0× 2 3 +1× 2 2 +0× 2 1 +0× 2 0$

$fifth hexadecimal digit=0×8+1×4+0×2+0×1$

$fifth hexadecimal digit=0+4+0+0$

$fifth hexadecimal digit=4$

$sixth hexadecimal digit=0× 2 3 +1× 2 2 +0× 2 1 +0× 2 0$

$sixth hexadecimal digit=0×8+1×4+0×2+0×1$

$sixth hexadecimal digit=0+4+0+0$

$sixth hexadecimal digit=4$

$So hexadecimal of given binary number = 749.A 44 16$

Answer 6

Chapter 85, Problem 18A

To determine

To express:

A binary number into a hexadecimal number.

Expert Solution & Answer

Answer to Problem 18A

Hexadecimal number is 749.A44₁₆.

Explanation of Solution

Given information:

A binary number 11101001001.1010010001₂.

Calculation:

Binary number system uses the number 2 as its base. Therefore, it has 2 symbols: The numbers are 0 and 1.

And a hexadecimal number system uses the number 16 as its base i.e. it has 16 symbols, hexadecimal digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F.

Binary numbers are represented as from hexadecimal number

Binary	0000	0001	0010	0011	0100	0101	0110	0111
Decimal	0	1	2	3	4	5	6	7
Hexadecimal	0	1	2	3	4	5	6	7

Binary	1000	1001	1010	1011	1100	1101	1110	1111
Decimal	8	9	10	11	12	13	14	15
Hexadecimal	8	9	A	B	C	D	E	F

Each hexadecimal digit consists of 4 binary digits.

For example, hexadecimal number 9 is equal to binary number 1001.

For converting integer part of binary number into hexadecimal number, write down the binary number and represent four binary digits from right by its hexadecimal digit from the table.

Then combine all the digits together.

For converting fractional part of binary number into hexadecimal number, write down the binary number and represent four binary digits from left by its hexadecimal digit from the table.

Then combine all the digits together.

Finally, hexadecimal number is combination of both integer and fractional part.

Hexadecimal digits are equal to the summation of 2ⁿ where n = 0, 1, 2 and 3 (position from right).

For example, 9 = 2³+2⁰. In this example, 2¹ and 2²are not there. So, at position 1 and 2, binary digit is zero, and at position 0 and 3, binary digit is one. Therefore, hexadecimal of binary 1001 is

Mathematics For Machine Technology, Chapter 85, Problem 18A

The hexadecimal number is equal to the summation of binary digits d_n × 2ⁿ

Divide the binary number into block of four digits. If four digits are not there, then add additional zero in binary number. For example, 11 is written as 0011 and .11 is written as .1100.

Hexadecimal of binary number 1100100101001011.1001001001₂ is (Starting from right for integer part and starting from left for fractional part)

$binary number= 0111 0100 1001 . 1010 0100 0100 →six hexadecimal digits are exist$

$first hexadecimal digit=0× 2 3 +1× 2 2 +1× 2 1 +1× 2 0$

$first hexadecimal digit=0×8+1×4+1×2+1×1$

$first hexadecimal digit=0+4+2+1$

$first hexadecimal digit=7$

$second hexadecimal digit=0× 2 3 +1× 2 2 +0× 2 1 +0× 2 0$

$second hexadecimal digit=0×8+1×4+0×2+0×1$

$second hexadecimal digit=0+4+0+0$

$second hexadecimal digit=4$

$third hexadecimal digit=1× 2 3 +0× 2 2 +0× 2 1 +1× 2 0$

$third hexadecimal digit=1×8+0×4+0×2+1×1$

$third hexadecimal digit=8+0+0+1$

$third hexadecimal digit=9$

$fourth hexadecimal digit=1× 2 3 +0× 2 2 +1× 2 1 +0× 2 0$

$fourth hexadecimal digit=1×8+0×4+1×2+0×1$

$fourth hexadecimal digit=8+0+2+0$

$fourth hexadecimal digit=10=A$

$fifth hexadecimal digit=0× 2 3 +1× 2 2 +0× 2 1 +0× 2 0$

$fifth hexadecimal digit=0×8+1×4+0×2+0×1$

$fifth hexadecimal digit=0+4+0+0$

$fifth hexadecimal digit=4$

$sixth hexadecimal digit=0× 2 3 +1× 2 2 +0× 2 1 +0× 2 0$

$sixth hexadecimal digit=0×8+1×4+0×2+0×1$

$sixth hexadecimal digit=0+4+0+0$

$sixth hexadecimal digit=4$

$So hexadecimal of given binary number = 749.A 44 16$

Answer 7

Chapter 85, Problem 18A

To determine

To express:

A binary number into a hexadecimal number.

Answer 8

Expert Solution & Answer

Answer to Problem 18A

Hexadecimal number is 749.A44₁₆.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

Given information:

A binary number 11101001001.1010010001₂.

Calculation:

Binary number system uses the number 2 as its base. Therefore, it has 2 symbols: The numbers are 0 and 1.

And a hexadecimal number system uses the number 16 as its base i.e. it has 16 symbols, hexadecimal digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F.

Binary numbers are represented as from hexadecimal number

Binary	0000	0001	0010	0011	0100	0101	0110	0111
Decimal	0	1	2	3	4	5	6	7
Hexadecimal	0	1	2	3	4	5	6	7

Binary	1000	1001	1010	1011	1100	1101	1110	1111
Decimal	8	9	10	11	12	13	14	15
Hexadecimal	8	9	A	B	C	D	E	F

Each hexadecimal digit consists of 4 binary digits.

For example, hexadecimal number 9 is equal to binary number 1001.

For converting integer part of binary number into hexadecimal number, write down the binary number and represent four binary digits from right by its hexadecimal digit from the table.

Then combine all the digits together.

For converting fractional part of binary number into hexadecimal number, write down the binary number and represent four binary digits from left by its hexadecimal digit from the table.

Then combine all the digits together.

Finally, hexadecimal number is combination of both integer and fractional part.

Hexadecimal digits are equal to the summation of 2ⁿ where n = 0, 1, 2 and 3 (position from right).

For example, 9 = 2³+2⁰. In this example, 2¹ and 2²are not there. So, at position 1 and 2, binary digit is zero, and at position 0 and 3, binary digit is one. Therefore, hexadecimal of binary 1001 is

Mathematics For Machine Technology, Chapter 85, Problem 18A

The hexadecimal number is equal to the summation of binary digits d_n × 2ⁿ

Divide the binary number into block of four digits. If four digits are not there, then add additional zero in binary number. For example, 11 is written as 0011 and .11 is written as .1100.

Hexadecimal of binary number 1100100101001011.1001001001₂ is (Starting from right for integer part and starting from left for fractional part)

$binary number= 0111 0100 1001 . 1010 0100 0100 →six hexadecimal digits are exist$

$first hexadecimal digit=0× 2 3 +1× 2 2 +1× 2 1 +1× 2 0$

$first hexadecimal digit=0×8+1×4+1×2+1×1$

$first hexadecimal digit=0+4+2+1$

$first hexadecimal digit=7$

$second hexadecimal digit=0× 2 3 +1× 2 2 +0× 2 1 +0× 2 0$

$second hexadecimal digit=0×8+1×4+0×2+0×1$

$second hexadecimal digit=0+4+0+0$

$second hexadecimal digit=4$

$third hexadecimal digit=1× 2 3 +0× 2 2 +0× 2 1 +1× 2 0$

$third hexadecimal digit=1×8+0×4+0×2+1×1$

$third hexadecimal digit=8+0+0+1$

$third hexadecimal digit=9$

$fourth hexadecimal digit=1× 2 3 +0× 2 2 +1× 2 1 +0× 2 0$

$fourth hexadecimal digit=1×8+0×4+1×2+0×1$

$fourth hexadecimal digit=8+0+2+0$

$fourth hexadecimal digit=10=A$

$fifth hexadecimal digit=0× 2 3 +1× 2 2 +0× 2 1 +0× 2 0$

$fifth hexadecimal digit=0×8+1×4+0×2+0×1$

$fifth hexadecimal digit=0+4+0+0$

$fifth hexadecimal digit=4$

$sixth hexadecimal digit=0× 2 3 +1× 2 2 +0× 2 1 +0× 2 0$

$sixth hexadecimal digit=0×8+1×4+0×2+0×1$

$sixth hexadecimal digit=0+4+0+0$

$sixth hexadecimal digit=4$

$So hexadecimal of given binary number = 749.A 44 16$

Answer 12

Ch. 85 - Prob. 1A Ch. 85 - Prob. 2A Ch. 85 - Prob. 3A Ch. 85 - Prob. 4A Ch. 85 - Prob. 5A Ch. 85 - Prob. 6A Ch. 85 - Prob. 7A Ch. 85 - Prob. 8A Ch. 85 - Prob. 9A Ch. 85 - Prob. 10A

To express: A binary number into a hexadecimal number.

Concept explainers

Videos

To express:

A binary number into a hexadecimal number.

Answer to Problem 18A

Explanation of Solution

Want to see more full solutions like this?

Chapter 85 Solutions