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Recent questions tagged number-representation

25 votes
2 answers
331
GATE IT 2004 | Question: 43
The number $(123456)_8$ is equivalent to $\text{(A72E)}_{16}$ and $(22130232)_4$ $\text{(A72E)}_{16}$ and $(22131122)_4$ $\text{(A73E)}_{16}$ and $(22130232)_4$ $\text{(A62E)}_{16}$ and $(22120232)_4$
The number $(123456)_8$ is equivalent to$\text{(A72E)}_{16}$ and $(22130232)_4$$\text{(A72E)}_{16}$ and $(22131122)_4$$\text{(A73E)}_{16}$ and $(22130232)_4$$\text{(A62E)...
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26 votes
4 answers
332
GATE IT 2004 | Question: 42
Using a $4-bit$ $2's$ complement arithmetic, which of the following additions will result in an overflow? $1100 + 1100$ $0011 + 0111$ $1111 + 0111$ i only ii only iii only i and iii only
Using a $4-bit$ $2's$ complement arithmetic, which of the following additions will result in an overflow?$1100 + 1100$$0011 + 0111$$1111 + 0111$i onlyii onlyiii onlyi and...
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24 votes
3 answers
333
GATE IT 2006 | Question: 7, ISRO2009-41
The addition of $4-bit$, two's complement, binary numbers $1101$ and $0100$ results in $0001$ and an overflow $1001$ and no overflow $0001$ and no overflow $1001$ and an overflow
The addition of $4-bit$, two's complement, binary numbers $1101$ and $0100$ results in$0001$ and an overflow$1001$ and no overflow$0001$ and no overflow$1001$ and an over...
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31 votes
2 answers
334
GATE IT 2007 | Question: 42
$(C012.25)_H - (10111001110.101)_B =$ $(135103.412)_o$ $(564411.412)_o$ $(564411.205)_o$ $(135103.205)_o$
$(C012.25)_H - (10111001110.101)_B =$$(135103.412)_o$$(564411.412)_o$$(564411.205)_o$$(135103.205)_o$
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31 votes
6 answers
339
GATE CSE 1995 | Question: 2.12, ISRO2015-9
The number of $1$'s in the binary representation of $(3\ast4096 + 15\ast256 + 5\ast16 + 3)$ are: $8$ $9$ $10$ $12$
The number of $1$'s in the binary representation of $(3\ast4096 + 15\ast256 + 5\ast16 + 3)$ are:$8$$9$$10$$12$
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21 votes
2 answers
340
GATE CSE 1994 | Question: 2.7
Consider $n$-bit (including sign bit) $2's$ complement representation of integer numbers. The range of integer values, $N$, that can be represented is ______ $\leq N \leq $______ .
Consider $n$-bit (including sign bit) $2's$ complement representation of integer numbers. The range of integer values, $N$, that can be represented is ______ $\leq N \leq...
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20 votes
3 answers
341
GATE CSE 1993 | Question: 6.5
Convert the following numbers in the given bases into their equivalents in the desired bases: $(110.101)_{2} = (x)_{10} $ $(1118)_{10} = (y)_{H}$
Convert the following numbers in the given bases into their equivalents in the desired bases:$(110.101)_{2} = (x)_{10} $$(1118)_{10} = (y)_{H}$
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27 votes
2 answers
342
GATE CSE 1997 | Question: 5.4
Given $\sqrt{(224)_r} =(13)_r$. The value of the radix $r$ is: $10$ $8$ $5$ $6$
Given $\sqrt{(224)_r} =(13)_r$.The value of the radix $r$ is:$10$$8$$5$$6$
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53 votes
3 answers
343
GATE CSE 2010 | Question: 8
$P$ is a $16$-bit signed integer. The $2$'s complement representation of $P$ is $(F87B)_{16}$. The $2$'s complement representation of $8\times P$ is $(C3D8)_{16}$ $(187B)_{16}$ $(F878)_{16}$ $(987B)_{16}$
$P$ is a $16$-bit signed integer. The $2$'s complement representation of $P$ is $(F87B)_{16}$. The $2$'s complement representation of $8\times P$ is$(C3D8)_{16}$$(187B)_{...
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33 votes
3 answers
345
GATE CSE 2014 Set 2 | Question: 8
Consider the equation $(123)_5=(x8)_y$ with $x$ and $y$ as unknown. The number of possible solutions is _____ .
Consider the equation $(123)_5=(x8)_y$ with $x$ and $y$ as unknown. The number of possible solutions is _____ .
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34 votes
3 answers
348
GATE CSE 2014 Set 1 | Question: 8
The base (or radix) of the number system such that the following equation holds is____________. $\frac{312}{20} = 13.1$
The base (or radix) of the number system such that the following equation holds is____________. $\frac{312}{20} = 13.1$
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31 votes
2 answers
350
GATE CSE 1998 | Question: 1.17
The octal representation of an integer is $(342)_8$. If this were to be treated as an eight-bit integer in an $8085$ based computer, its decimal equivalent is $226$ $-98$ $76$ $-30$
The octal representation of an integer is $(342)_8$. If this were to be treated as an eight-bit integer in an $8085$ based computer, its decimal equivalent is$226$$-98$$7...
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22 votes
2 answers
351
GATE CSE 1999 | Question: 2.17
Zero has two representations in Sign-magnitude $2's$ complement $1's$ complement None of the above
Zero has two representations inSign-magnitude$2's$ complement$1's$ complementNone of the above
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29 votes
4 answers
352
GATE CSE 1999 | Question: 1.20
Booth's coding in $8$ bits for the decimal number $-57$ is: $0-100+1000$ $0-100+100-1$ $0-1+100-10+1$ $00-10+100-1$
Booth's coding in $8$ bits for the decimal number $-57$ is:$0-100+1000$$0-100+100-1$$0-1+100-10+1$$00-10+100-1$
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21 votes
2 answers
353
GATE CSE 2013 | Question: 4
The smallest integer that can be represented by an $8\text{-bit}$ number in $2's$ complement form is $-256$ $-128$ $-127$ $0$
The smallest integer that can be represented by an $8\text{-bit}$ number in $2's$ complement form is$-256$$-128$ $-127$$0$
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20 votes
2 answers
355
GATE CSE 2005 | Question: 17
The hexadecimal representation of (657)8 is: $\text{1AF}$ $\text{D78}$ $\text{D71}$ $\text{32F}$
The hexadecimal representation of (657)8 is:$\text{1AF}$$\text{D78}$$\text{D71}$$\text{32F}$
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25 votes
6 answers
357
GATE CSE 2009 | Question: 5, ISRO2017-57
$(1217)_8$ is equivalent to $(1217)_{16}$ $(028F)_{16}$ $(2297)_{10}$ $(0B17)_{16}$
$(1217)_8$ is equivalent to$(1217)_{16}$$(028F)_{16}$$(2297)_{10}$$(0B17)_{16}$
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27 votes
5 answers
358
GATE CSE 2004 | Question: 66
Let $A = 1111 1010$ and $B = 0000 1010$ be two $8-bit$ $2’s$ complement numbers. Their product in $2’s$ complement is $1100 0100$ $1001 1100$ $1010 0101$ $1101 0101$
Let $A = 1111 1010$ and $B = 0000 1010$ be two $8-bit$ $2’s$ complement numbers. Their product in $2’s$ complement is$1100 0100$$1001 1100$$1010 0101$$1101 0101$
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19 votes
2 answers
360
GATE CSE 2004 | Question: 19
If $73_x$ (in base-x number system) is equal to $54_y$ (in base $y$-number system), the possible values of $x$ and $y$ are $8, 16$ $10, 12$ $9, 13$ $8, 11$
If $73_x$ (in base-x number system) is equal to $54_y$ (in base $y$-number system), the possible values of $x$ and $y$ are$8, 16$$10, 12$$9, 13$$8, 11$
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