Mathematics for Machine Technology
Mathematics for Machine Technology
7th Edition
ISBN: 9781133281450
Author: John C. Peterson, Robert D. Smith
Publisher: Cengage Learning
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Chapter 83, Problem 16A
To determine

To express:

A binary number into a hexadecimal number.

Expert Solution & Answer
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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

    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 83, Problem 16A

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= 0001 0000 1010 1011 . 1001 0010 0110 sevenhexadecimaldigitsareexist

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

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

   firsthexadecimaldigit=0+0+0+1

   firsthexadecimaldigit=1

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

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

   secondhexadecimaldigit=0+0+0+0

   secondhexadecimaldigit=0

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

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

   thirdhexadecimaldigit=8+0+2+0

   thirdhexadecimaldigit=10=A

   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

   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

   seventhhexadecimaldigit=0× 2 3 +1× 2 2 +1× 2 1 +0× 2 0

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

   seventhhexadecimaldigit=0+4+2+0

   seventhhexadecimaldigit=6

   Sohexadecimalofgivenbinarynumber=10AB .926 16

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