Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Chapter 86, Problem 45A
To determine

Conversion of Excess-3 code numbers 1010 0110.0011 0101 to a decimal numbers.

Expert Solution & Answer
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Answer to Problem 45A

Decimal numbers is 73.0210.

Explanation of Solution

Given information:

An Excess-3 code numbers 1010 0110.0011 0101.

Calculation:

Excess-3 code is unweighted code.

In excess-3 code decimal numbers are obtained by converting 4 bit binary numbers into decimal numbers and then subtracting 3 in each decimal digit.

Excess-3 code number system uses 2 symbols: The numbers are 0 and 1.

And a decimal number system uses the number 10 as its base i.e. it has 10 symbols; decimal digits are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

Each decimal digit consists of 4 bits excess-3 code.

Excess-3 code numbers are represented as from decimal number

    Excess-3 code0011010001010110011110001001101010111100
    Binary code0000000100100011010001010110011110000101
    Decimal0123456789

Decimal of excess-3 code numbers 1010 0110.0011 0101 is (Starting from right for integer part and starting from left for fractional part)

Excess3codenumber= 1010 0110 . 0011 0101 fourdecimaldigitsareexist

firstdecimaldigit=1× 2 3 +0× 2 2 +1× 2 1 +0× 2 0

firstdecimaldigit=1×8+0×4+1×2+0×1

firstdecimaldigit=8+0+2+0

firstdecimaldigit=10

forexcess3codedecimaldigit=103=7

seconddecimaldigit=0× 2 3 +1× 2 2 +1× 2 1 +0× 2 0

seconddecimaldigit=0×8+1×4+1×2+0×1

seconddecimaldigit=0+4+2+0

seconddecimaldigit=6

forexcess3codedecimaldigit=63=3

thirddecimaldigit=0× 2 3 +0× 2 2 +1× 2 1 +1× 2 0

thirddecimaldigit=0×8+0×4+1×2+1×1 thirddecimaldigit=0+0+2+1 thirddecimaldigit=3

forexcess3codedecimaldigit=33=0 fourthdecimaldigit=0× 2 3 +1× 2 2 +0× 2 1 +1× 2 0 fourthdecimaldigit=0×8+1×4+0×2+1×1 fourthdecimaldigit=0+4+0+1

fourthdecimaldigit=5 forexcess3codedecimaldigit=53=2 Sodecimalofgivenexcess3codenumber= 73.02 10

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