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Convert decimal number 199.375 into binary, octal, hexadecimal system

Mumbai University > Computer Engineering > Sem 3 > DIGITAL LOGIC DESIGN & ANALYSIS Marks : 2M Year: May16

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(1). Convert decimal number 199.375 into Binary system

$(199.375)_{10}$ =$(?)_2$

Solution:

Whole number part: 199

Remainder
2 199 1 (199/2=99+1)
2 99 1
2 49 1
2 24 0
2 12 0
2 6 0
2 3 1
2 1 1 (1/2=0+1)

(Starting with the bottom remainder, read the sequence of remainders upwards to the top)

Therefore, $(199)_{10}$ =$(11000111)_2$

Fractional Part: 0.375

Whole Number
0.375*2 0.75 0
(0.75-0)*2 1.5 1
(1.5-0)*2 1 1

Therefore, $(0.375)_{10}$ =$(0.011)_2$

Result: $(199.375)_{10}$ =$(11000111.011)_2$

(2). Convert decimal number 199.375 into Octal system

$(199.375)_{10}$ =$(?)_8$

Solution:

$(199.375)_{10}$

=$(11000111)_2$ … from (1)

=$(011 000 111)_2$

=$(307)_8$

Result: $(199.375)_{10}$ =$(307)_8$

(3). Converting decimal number 199.375 into Hexadecimal system

$(199.375)_{10}$ =$(?)_{16}$

Solution:

$(199.375)_{10}$

=$(11000111)_2$ … from (1)

=$(1100 0111)_2$

=$(C7)_{16}$

Result: $(199.375)_10$ =$(C7)_{16}$

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