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Recent questions tagged number-representation

2 2 votes
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156
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two's complement number
𝐺𝑖𝑣𝑒𝑛 𝑡ℎ𝑒 4-𝑏𝑖𝑡 𝑡𝑤𝑜'𝑠 𝑐𝑜𝑚𝑝𝑙𝑒𝑚𝑒𝑛𝑡 𝑛𝑢𝑚𝑏𝑒𝑟 𝑋 = 𝑥₃𝑥₂𝑥₁𝑥₀, 𝑤𝑟𝑖𝑡𝑒 𝑡ℎ𝑒 𝑠𝑖𝑚𝑝𝑙𝑒𝑠𝑡 𝑆𝑂𝑃 𝑒𝑥𝑝𝑟𝑒𝑠𝑠𝑖𝑜𝑛 𝑓𝑜𝑟 𝑒𝑎𝑐ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑜𝑙𝑙𝑜𝑤𝑖𝑛𝑔:𝑎. 𝑜𝑑𝑑 (𝑠ℎ𝑜𝑢𝑙𝑑 𝑏𝑒 1 𝑤ℎ𝑒𝑛 𝑋 𝑖𝑠 𝑜𝑑𝑑 𝑎𝑛𝑑 0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒):𝑏. 𝑒𝑣...
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1 1 vote
1 answers 1 answer
127
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Two's complement form question (University of Virginia)
Let s₈ be the number of distinct numbers that can be represented as signed (two’s-complement) 1-byte integers and u₈ be the number of distinct numbers that can be represe...
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1 1 vote
0 0 answers
114
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IEEE representation question (University of Virginia)
Let f₃₂ be the number of distinct numbers that can be represented in 4-byte IEEE-style floating point and u₃₂ be the number of distinct numbers that can be represented as...
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5 5 votes
4 4 answers
295
295 views
GO Classes DPP | GATE CS | Digital Logic | Base Arithmetic
In the following hexadecimal addition, find the digit $x$. $$(4x\mathrm{D})_{16}+(2\mathrm{B}7)_{16}=(744)_{16}$$
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6 6 votes
2 2 answers
224
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GO Classes DPP | GATE CS | Digital Logic | Complement Values
How many $8$-bit patterns represent the same decimal value when interpreted as sign-magnitude and $1$'s complement numbers?$64$ $127$ $128$ $255$
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5 5 votes
2 2 answers
184
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GO Classes DPP | GATE CS | Digital Logic | Representation Change
An $8$-bit pattern represents $-45$ in $2$'s complement form. If the same bit pattern is interpreted as a $1$'s complement number, what decimal value does it represent?$-...
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5 5 votes
2 2 answers
195
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GO Classes DPP | GATE CS | Digital Logic | Shift Overflow
Consider an $8$-bit signed integer system using $2$’s complement representation. For how many integer values of $x$ does the arithmetic left shift operation $(x << 1$, i....
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4 4 votes
1 1 answer
166
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GO Classes DPP | GATE CS | Digital Logic | Number Representation
Let $X$ be an $8$-bit integer stored in $2$'s complement representation. If the hexadecimal value of $X$ is given as $(E4)_{16}$, what is the decimal equivalent of the va...
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7 7 votes
1 1 answer
265
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GO Classes DPP | GATE CS | Digital Logic | Binary Fractions
Which of the following exact decimal expressions can be represented in binary notation with a finite number of bits?$0.84-0.33$ $0.64-0.015$ $0.72+0.02$ $0.45-0.125$
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10 10 votes
2 2 answers
289
289 views
GO Classes DPP | GATE CS | Digital Logic | Parity Counting
In a $10$-bit $2$’s complement system, how many bit patterns represent negative integers that are divisible by $8$, not divisible by $16$, and have even parity?
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4 4 votes
2 2 answers
215
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GO Classes DPP | GATE CS | Digital Logic | Two’s Complement
Which of the following $2$’s complement bit strings represents the smallest decimal value? Each bit string must be interpreted using its own given bit-width.$1001011$ as ...
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4 4 votes
1 1 answer
192
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GO Classes DPP | GATE CS | Digital Logic | Signed Bit Operations
A $12$-bit $2$’s complement number has hexadecimal representation $(B6D)_H$. This number is sign-extended to $16$ bits and then arithmetic right-shifted by $2$ positions....
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5 5 votes
2 2 answers
279
279 views
GO Classes DPP | GATE CS | Digital Logic | Two's Complement Overflow
Suppose we have two $16$-bit $2$’s complement numbers:$$101xx101101xxxxx$$$$1101101xx11xxxxx$$Here, each $x$ is an independent unknown bit and can be either $0$ or $1$.Co...
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4 4 votes
3 3 answers
299
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GO Classes DPP | GATE CS | Digital Logic | Base Conversion
Find the base $r$ if $(132)_r+(45)_r=(221)_r$
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2 2 votes
3 3 answers
238
238 views
GO Classes DPP | GATE CS | Digital Logic | Minimum Bit Encoding
A controller has to send one of $45$ possible status messages. Each message is encoded using a fixed-length binary code. What is the minimum number of bits required, and ...
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3 3 votes
2 2 answers
247
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GO Classes DPP | GATE CS | Digital Logic | Two’s Complement Encoding
What is the minimum number of bits required to represent $-92$ in $2$’s complement form, and what is its representation using that minimum number of bits?$7$ bits, $01001...
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3 3 votes
3 3 answers
197
197 views
GO Classes DPP | GATE CS | Digital Logic | Hex Signed Conversion
What decimal value is represented by the following $8$-bit $2$’s complement bit pattern, given in hexadecimal notation?$$A7_{16}=\_\_\_\_\_\_\_\__{10}$$
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1 1 vote
3 3 answers
275
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GO Classes DPP | GATE CS | Digital Logic | Overflow Detection
In a $5$-bit $2$’s complement system, which of the following additions result in overflow?$11+9$ $-13+(-7)$ $14+(-6)$ $-9+12$
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4 4 votes
2 2 answers
216
216 views
GO Classes DPP | GATE CS | Digital Logic | Signed Binary Arithmetic
An $8$-bit $2$’s complement number is given as $10010110$. Find its decimal value.
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4 4 votes
1 1 answer
181
181 views
GO Classes DPP | GATE CS | Digital Logic | Signed Number Representation
In an $n$-bit signed number system, zero has exactly $2$ different representations in which of the following representations?Sign-magnitude and $1$’s complement only $2$’...
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8 8 votes
2 2 answers
234
234 views
GO Classes DPP | GATE CS | Digital Logic | Signed Number Representation
Let $X$ be the number of distinct $12$-bit integers representable in $2$’s complement form. Let $Y$ be the number of distinct $12$-bit integers representable in $1$’s com...
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7 7 votes
3 3 answers
944
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GATE DA 2026 | GA | Question: 2
The product of the digits of a three-digit number is $70$. The sum of the digits of this three-digit number is $\_\_\_\_$$12$$14$$16$$18$
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9 9 votes
5 5 answers
2.6k
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GATE CSE 2026 | Set 2 | Question: 18
In a system, numbers are represented using $4$-bit two's complement form. Consider four numbers $N 1=1011, N 2=1101, N 3=1010$ and $N 4=1001$ in the system. Which of the ...
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10 10 votes
3 answers 3 answers
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GATE CSE 2026 | Set 1 | Question: 12
Consider the $8$ -bit signed integers $X, Y$ and $Z$ represented using the sign-magnitude form. The binary representations of $X$ and $Y$ are as follows:\[X: 10110100 \qu...
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3 3 votes
2 2 answers
545
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Practice Type | Computer Organisation | Floating Point Representation |
P and Q are 32 bit registers used to store IEEE single precision floating point notations (32 bit).Let content of P and Q are P = C0400000H and Q = 40400000H. The P * Q r...
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2 2 votes
2 answers 2 answers
392
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What should be the answer for this question
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118
118 views
UPSC CBI 2025 | Assistant Programmer | Question: 83
What is the output if the following JavaScript program is executed by a typical web browser?// LocalScope.js var j=6; // global variable declaration and initialization fu...
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2 2 votes
2 2 answers
590
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UGC NET CSE | June 2025 | Part 2 | Question: 6
Binary equivalent to $(\mathrm{AOF})_{16}$ is:$111000111$$101001111$$101000001111$$111100001010$
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1 1 vote
1 1 answer
421
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UGC NET CSE | June 2025 | Part 2 | Question: 34
CB84000D001C001C is the content of a UDP header in hexadecimal format. The source port number is$52100$$13$$28$$52000$
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2 2 votes
1 1 answer
293
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UGC NET CSE | January 2025 | Part 2 | Question: 20
Match the LIST-I with LIST-II$\begin{array}{|l|l|l|l|} \hline & \textbf{LIST-I} & & \textbf{LIST-II} \\ \hline \text{A.} & (100110011)_{2} & \text{I.} & \text{Error detec...
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