written 7.3 years ago by | • modified 4.6 years ago |
Mumbai University > Computer Engineering > Sem 3 > DIGITAL LOGIC DESIGN & ANALYSIS Marks : 2M Year: May16
written 7.3 years ago by | • modified 4.6 years ago |
Mumbai University > Computer Engineering > Sem 3 > DIGITAL LOGIC DESIGN & ANALYSIS Marks : 2M Year: May16
written 5.4 years ago by |
(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: $(199.375)_10$ =$(C7)_{16}$