
Concept explainers
To express:
A binary number into a hexadecimal number.

Answer to Problem 16A
Hexadecimal number is 10AB.92616.
Explanation of Solution
Given information:
A binary number 1000010101011.100100100112.
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. The 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
The hexadecimal number is equal to the summation of binary digits dn × 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)
Want to see more full solutions like this?
Chapter 83 Solutions
Mathematics for Machine Technology
- Convert 101101₂ to base 10arrow_forwardDefinition: A topology on a set X is a collection T of subsets of X having the following properties. (1) Both the empty set and X itself are elements of T. (2) The union of an arbitrary collection of elements of T is an element of T. (3) The intersection of a finite number of elements of T is an element of T. A set X with a specified topology T is called a topological space. The subsets of X that are members of are called the open sets of the topological space.arrow_forward2) Prove that for all integers n > 1. dn 1 (2n)! 1 = dxn 1 - Ꮖ 4 n! (1-x)+/arrow_forward
- Definition: A topology on a set X is a collection T of subsets of X having the following properties. (1) Both the empty set and X itself are elements of T. (2) The union of an arbitrary collection of elements of T is an element of T. (3) The intersection of a finite number of elements of T is an element of T. A set X with a specified topology T is called a topological space. The subsets of X that are members of are called the open sets of the topological space.arrow_forwardDefinition: A topology on a set X is a collection T of subsets of X having the following properties. (1) Both the empty set and X itself are elements of T. (2) The union of an arbitrary collection of elements of T is an element of T. (3) The intersection of a finite number of elements of T is an element of T. A set X with a specified topology T is called a topological space. The subsets of X that are members of are called the open sets of the topological space.arrow_forward3) Let a1, a2, and a3 be arbitrary real numbers, and define an = 3an 13an-2 + An−3 for all integers n ≥ 4. Prove that an = 1 - - - - - 1 - - (n − 1)(n − 2)a3 − (n − 1)(n − 3)a2 + = (n − 2)(n − 3)aı for all integers n > 1.arrow_forward
- Definition: A topology on a set X is a collection T of subsets of X having the following properties. (1) Both the empty set and X itself are elements of T. (2) The union of an arbitrary collection of elements of T is an element of T. (3) The intersection of a finite number of elements of T is an element of T. A set X with a specified topology T is called a topological space. The subsets of X that are members of are called the open sets of the topological space.arrow_forwardDefinition: A topology on a set X is a collection T of subsets of X having the following properties. (1) Both the empty set and X itself are elements of T. (2) The union of an arbitrary collection of elements of T is an element of T. (3) The intersection of a finite number of elements of T is an element of T. A set X with a specified topology T is called a topological space. The subsets of X that are members of are called the open sets of the topological space.arrow_forwardDefinition: A topology on a set X is a collection T of subsets of X having the following properties. (1) Both the empty set and X itself are elements of T. (2) The union of an arbitrary collection of elements of T is an element of T. (3) The intersection of a finite number of elements of T is an element of T. A set X with a specified topology T is called a topological space. The subsets of X that are members of are called the open sets of the topological space.arrow_forward
- Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,
