The binary string 11010111100101 is a floating-point number expressed using the 14-bit simple model given in your text. What is its decimal equivalent?
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- (a) If I have an n-bit unsigned integer, is it correct to say that I can always represent it as an (n + 1)-bit signed integer? Discuss briefly, in your own words. (b) If I have an m-bit signed integer, and I know its value is negative, I can use the NEG operation; then, since its sign bit will now be 0, I should be able to represent the value as an (m − 1)-bit unsigned integer, simply by dropping the leading 0. Is this correct? Discuss briefly, in your own words.Is it possible to convert 16-bit binary data to 8-bit binary data such as: 1111111011111110 -> this 16 bit to 8 bit? If possible then do it and mention the converted binary number.Write a program to print out the binary equivalent of a positive integer value entered. [Reverse binary string is accepted as output. For example, the binary of 4561 is 1000111010001 but if the user outputs it in reverse, i.e., 1000101110001, it is accepted. Just mention that LSB is the left most bit]
- 1. Floating Point Numbersa. Show the difference between IEEE 16, 32, 64, 128-bit floating-point numbers.b. Express the following numbers in hexadecimal IEEE 32-bit floating-pointformat. i. 320ii. -622. Design a circuit that implements function p below using AND, OR, and NOT gates.DO NOT change the form of the equation. ?(?0, ?1, ?2, ) = {?2(?0?1 + ?̅0?̅1)}. (?̅2 + ?̅1)4. Show how the unsigned serial multiplication method would compute M × Q where M = 10110and Q = 01101. M and Q are unsigned numbers. For each step, describe in words what is happening (shift left, shift right, add/subtract M or Q into product, set a bit, etc.), and showthe product (or partial product) for that step. (Note: Q is the multiplier and M is themultiplicand.)Scenario: In a biased N-bit binary number system with bias B, positive and negative numbers are represented as their value plus the bias B. For example, for 5-bit numbers with a bias of 15, the number 0 is represented as 01111, 1 as 10000, and so forth. Biased number systems are sometimes used in floating point mathematics. Consider a biased 8-bit binary number system with a bias of 12710 Question: What is the representation and value of the most positive number?What is the largest binary number that can be expressed with 16 bits? What are the equivalent decimal and hexadecimal numbers?
- Use IEEE 754 single-precision standard (32 bits) to represent (-131.8125)10, and then convert it to Hexadecimal. Now assume we are defining new 16-bit floating-point representations as shown in the figure below. Let X = 0x50A2 and Y = 0x3980 are two 16-bit floating-point numbers, represented in this format. Sign (1 bit) Exponent (5 bits) Significant (10 bits) Find the values of X and Y in decimal? Let Z = X+Y. Find 16-bit floating-point representation (in Hex) of Z? (Show how the floating-point addition is performed step by step).Question 5 a) Briefly explain the Nyquist theorem in the context of digital sampling. b) Using logic gates, design an active low chip select for the memory a 256 K memory device starting at address 38000016 in a 16 Megabyte memory space. c) Convert each of the following 8-bit signed magnitude binary numbers to decimal. i) 10110101(base 2) ii) 01000101(base 2) iii) 11101010(base 2) iv) 01011110(base 2)For the decimal number 2007, in the binary representation, suppose your bits are the input of a combinational circuit. Develop this circuit with at least 3 layers, so that the combination of bits across the circuit will result in logic level 1 as exit.
- Use Boolean algebra to simplify the following expression, then draw a logic gate circuit for the simplified expression:a) 13–9 b) –13 –13 Perform the above decimal arithmetic problems by first converting the numbers to binary, 2’s complement form (using a 7 bit word in every case). Then perform the 2’s compliment addition. Show the result in binary indicating as in the problem above whether each result is positive or negative or overflowed (by writing “positive”, “negative” or “overflow” next to the binary answer) and then follow with the decimal value of the result if there was no overflow.KINDLY ANSWER. THANKS Derive the Boolean expressions of one-bit comparator and two-bit comparators. How do you realize a higher magnitude comparator using lower bit comparator? Design a 2-bit comparator using a single Logic gate? Design an 8-bit comparator using two numbers of IC 7485?