Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
bartleby

Concept explainers

bartleby

Videos

Question
Book Icon
Chapter 85, Problem 17A
To determine

To express:

A binary number into a hexadecimal number.

Expert Solution & Answer
Check Mark

Answer to Problem 17A

Hexadecimal number is C94B.92416.

Explanation of Solution

Given information:

A binary number 1100100101001011.10010010012.

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

    Binary00000001001000110100010101100111
    Decimal01234567
    Hexadecimal01234567
    Binary10001001101010111100110111101111
    Decimal89101112131415
    Hexadecimal89ABCDEF

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 17A

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)

   binarynumber= 1100 1001 0100 1011 . 1001 0010 0100 sevenhexadecimaldigitsareexist

   firsthexadecimaldigit=1× 2 3 +1× 2 2 +0× 2 1 +0× 2 0

   firsthexadecimaldigit=1×8+1×4+0×2+0×1

   firsthexadecimaldigit=8+4+0+0

   firsthexadecimaldigit=12=C

   secondhexadecimaldigit=1× 2 3 +0× 2 2 +0× 2 1 +1× 2 0

   secondhexadecimaldigit=1×8+0×4+0×2+1×1

   secondhexadecimaldigit=8+0+0+1

   secondhexadecimaldigit=9

   thirdhexadecimaldigit=0× 2 3 +1× 2 2 +0× 2 1 +0× 2 0

   thirdhexadecimaldigit=0×8+1×4+0×2+0×1

   thirdhexadecimaldigit=0+4+0+0

   thirdhexadecimaldigit=4

   fourthhexadecimaldigit=1× 2 3 +0× 2 2 +1× 2 1 +1× 2 0

   fourthhexadecimaldigit=1×8+0×4+1×2+1×1

   fourthhexadecimaldigit=8+0+2+1

   fourthhexadecimaldigit=11=B

   fourthhexadecimaldigit=11=B

   fifthhexadecimaldigit=1× 2 3 +0× 2 2 +0× 2 1 +1× 2 0

   fifthhexadecimaldigit=1×8+0×4+0×2+1×1

   fifthhexadecimaldigit=8+0+0+1

   fifthhexadecimaldigit=9

   sixthhexadecimaldigit=0× 2 3 +0× 2 2 +1× 2 1 +0× 2 0

   sixthhexadecimaldigit=0×8+0×4+1×2+0×1

   sixthhexadecimaldigit=0+0+2+0

   sixthhexadecimaldigit=2

   sixthhexadecimaldigit=0× 2 3 +1× 2 2 +0× 2 1 +0× 2 0

   sixthhexadecimaldigit=0×8+1×4+0×2+0×1

   sixthhexadecimaldigit=0+4+0+0

   sixthhexadecimaldigit=4

   Sohexadecimalofgivenbinarynumber=C94B .924 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
Let A be a vector space with basis 1, a, b. Which (if any) of the following rules turn A into an algebra? (You may assume that 1 is a unit.) (i) a² = a, b² = ab = ba = 0. (ii) a²=b, b² = ab = ba = 0. (iii) a²=b, b² = b, ab = ba = 0.
No chatgpt pls will upvote
= 1. Show (a) Let G = Z/nZ be a cyclic group, so G = {1, 9, 92,...,g" } with g": that the group algebra KG has a presentation KG = K(X)/(X” — 1). (b) Let A = K[X] be the algebra of polynomials in X. Let V be the A-module with vector space K2 and where the action of X is given by the matrix Compute End(V) in the cases (i) x = p, (ii) xμl. (67) · (c) If M and N are submodules of a module L, prove that there is an isomorphism M/MON (M+N)/N. (The Second Isomorphism Theorem for modules.) You may assume that MON is a submodule of M, M + N is a submodule of L and the First Isomorphism Theorem for modules.
Knowledge Booster
Background pattern image
Advanced Math
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Mathematics For Machine Technology
Advanced Math
ISBN:9781337798310
Author:Peterson, John.
Publisher:Cengage Learning,
Propositional Logic, Propositional Variables & Compound Propositions; Author: Neso Academy;https://www.youtube.com/watch?v=Ib5njCwNMdk;License: Standard YouTube License, CC-BY
Propositional Logic - Discrete math; Author: Charles Edeki - Math Computer Science Programming;https://www.youtube.com/watch?v=rL_8y2v1Guw;License: Standard YouTube License, CC-BY
DM-12-Propositional Logic-Basics; Author: GATEBOOK VIDEO LECTURES;https://www.youtube.com/watch?v=pzUBrJLIESU;License: Standard Youtube License
Lecture 1 - Propositional Logic; Author: nptelhrd;https://www.youtube.com/watch?v=xlUFkMKSB3Y;License: Standard YouTube License, CC-BY
MFCS unit-1 || Part:1 || JNTU || Well formed formula || propositional calculus || truth tables; Author: Learn with Smily;https://www.youtube.com/watch?v=XV15Q4mCcHc;License: Standard YouTube License, CC-BY