Q2GATE 2021MCQ

If $(1235)_{x}\:=\:(3033)_{y}$ , where x and y indicate the bases of the corresponding numbers, then

📖 Explanation

$x^{3}+2 x^{2}+3 x+5=3 y^{3}+3 y+3$ Option (B) will satisfy the equation.

Q3GATE 2020MCQ

P, Q, and R are the decimal integers corresponding to the 4-bit binary number 1100 considered in signed magnitude, 1's complement, and 2's complement representations, respectively. The 6-bit 2's complement representation of (P+Q+R) is

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Q4GATE 2014NAT

The number of bytes required to represent the decimal number 1856357 in packed BCD (Binary Coded Decimal) form is_______.

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📖 Explanation

To represent decimal number into BCD number each decimal number is represented in 4 -bits while converting in BCD numbers, as

\begin{array}{ll}1 \rightarrow 0001 & 6 \rightarrow 0110 \\ 8 \rightarrow 1000 & 3 \rightarrow 0011 \\ 5 \rightarrow 0101 & 5 \rightarrow 0101 \\ & 7 \rightarrow 0111\end{array}

So total 4 bytes are required.

Q5GATE 2008MCQ

The two numbers represented in signed 2's complement form are P = 11101101 and Q = 11100110. If Q is subtracted from P, the value obtained in signed 2's complement is

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📖 Explanation

$\because$ Signed 2 's complement of

\begin{aligned} P&=11101101\\ \therefore \text{No.} \quad P&=00010011 \end{aligned}

$\because$ Signed 2 's complement of

\begin{aligned} Q &=11100110 \\ P-Q=P+(2 ' s& \text { complement of }Q) \\ &=00010011 \\ &\frac{+11100110}{11111001} \\ \text{2's complement of }\\ (P-Q)&=00000111 \end{aligned}

Q6GATE 2007MCQ

X = 01110 and Y =11001 are two 5-bit binary numbers represented in two's complement format. The sum of X and Y represented in two's complement format using 6 bits is

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📖 Explanation

\begin{array}{cccccccc} x &=&&0&1&1&1&0 \\ Y &=&&1&1&0&0&1 \\ x+y &=&1&0&0&1&1&1 \end{array}

Carry is discarded in the addition of numbers represented in 2's complement form. X + Y in 6 bits is 000111.

Q7GATE 2006MCQ

A new Binary Coded Pentary (BCP) number system is proposed in which every digit of a base-5 number is represented by its corresponding 3-bit binary code. For example, the base-5 number 24 will be represented by its BCP code 010100. In this numbering system, the BCP code 10001001101 corresponds of the following number is base-5 system

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📖 Explanation

$100010011001 \rightarrow 4231$

Q8GATE 2005MCQ

Decimal 43 in Hexadecimal and BCD number system is respectively

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📖 Explanation

(43)_{10}\rightarrow \begin{array}{c|c|c}16&43&\\ \hline16&2&B\\ \hline&0&2\\ \hline\end{array}

$\therefore (2B)_{H} (43)_{10}=(01000011)_{BCD}$

Q9GATE 2004MCQ

11001, 1001, 111001 correspond to the 2's complement representation of which one of the following sets of number

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📖 Explanation

$11001 \rightarrow 00111(+7)$ $1001 \rightarrow 0111(+7)$ $111001 \rightarrow 000111(+7)$ $\therefore$ Numbers given in question in 2 's complement correspond to -7