Digital Electronics Test 1

A binary number can be converted into decimal number by multiplying the binary numbers 1 or 0 by their weight and adding the product. Conversion of 101111 is done as follows:

On converting the decimal number (7864)₁₀ into hexadecimal number we obtain the result (EB8)₁₆ as follows:

In a signed 6-bit binary number representation, the range of numbers is determined by the most significant bit (MSB), which is used as the sign bit.

Here's a breakdown of the range calculation:

1. Signed 6-bit binary numbers use the first bit (MSB) as the sign bit:

   • 0 indicates a positive number
   • 1 indicates a negative number

2. Positive numbers (MSB is 0):

   • The remaining 5 bits represent the magnitude.
   • The smallest positive number is 000000 (0 in decimal).
   • The largest positive number is 011111 (31 in decimal).

3. Negative numbers (MSB is 1):

   • The 2's complement method is used to represent negative numbers.
   • The smallest negative number is 100000 (-32 in decimal).
   • The largest negative number is 111111 (-1 in decimal).

Thus, the range of numbers that can be represented using 6-bit signed binary number representation is from -32 to 31.

∴ The required 7-bit even parity Hamming code is ( 0 1 0 0 1 0 1).

Memory space = 2²⁰ × 24

Memory chip capacity = 2¹⁴ × 8

Now, the decimal number is converted into the number of base 7 as follows:

The three Boolean operators are NOT, OR, AND, These are also called basic gates for digital electronics.

\({V_0} = k\left[ {{2^{n - 1}}{b_{n - 1}} + {2^{n - 2}}{b_{n - 2}} + \ldots + 2{b_1} + {b_0}} \right]\)

b_nb_n-1...b₁b₀ are digits of digital input

V_FS = 10 V, n = 5

⇒ 10 = K [31]

K = 10/31

For Digital input (11011)₂

\({V_0} = \frac{{10}}{{31}}\left[ {27} \right]\)

= 8.71 V

NOT gate is used to invert the input signal.

In negative logic:

• logic 0 = Some positive voltage
• logic 1 = Zero voltage

or

• logic 0 = Some higher voltage level (i.e. + 5 V,)
• logic 1 = Some lower voltage level (i.e. + 2 V)

A in 1’s complement binary number system = (001010)₂

As the MSB is ‘0’, the number is positive.

Therefore, the number A = (001010)₂ = (10)₁₀

B in signed number system

B = (111010)₂

As the MSB is ‘1’, the number is negative.

Therefore the number B = (-26)₁₀

Now, X = A + B = (10)₁₀ + (-26)₁₀ = (-16)₁₀

The two’s complement representation of (-16)₁₀ is the two’s complement of (+16)₁₀

(+16)₁₀ = 010000

2’s complement = 110000

X in 2’s complement representation = (110000)₂

A + 1 = 1 (Always)

Hence,  option (c) is not correct.

POS form (Product of Sum form) of expression is suitable for circuit using NOR gates.

A multiplexer (or MUX) is a device that selects one of several analog or digital input signals and forwards the selected input into a single line, depending on the active select lines.

It is possible for an enable or strobe input to undergo an expansion of two or more MUX ICs to the digital multiplexer with the proficiency of large number of inputs.

Enable input is used to active the chip, when enable is high the chip works (ACTIVE), when enable is low the chip does not work (MEMORY). However, Enable can be Active-High or Active-Low, indicating it is active either when it is connected to VCC or GND respectively.

A digital multiplexer is a combinational circuit that selects one digital information from several sources and transmits the selected information on a single output line depending on the status of the select lines. That is why it is also known as a data selector.

If the number of n selected input lines is equal to 2^m then it requires m select lines to select one of m select lines.

A basic multiplexer principle can be demonstrated through the use of a rotary switch. Since its behaviour is similar to the multiplexer. There are around 10 digits out of which one is selected one at a time and fed to the output.