# 1. Represent -29.3125 in binary system. 16 bits. 9 for mantissa, 1 for sign, 5 for exponet, 1 for sign of exponet. 2. Write the data list that results from the shuffle-left algorithm to clen the following: 3, 0, 0,2, 6, 7, 0, 0, 5, 1.(include steps) 3. Assume a=1, b=2 c=3. What is the value of each Boolean expression?(true or false) (Show all steps). a. [(a+b)]>c] AND (b>=c) b. NOT[(a=b) AND (b=c)] 4.What numbers are compared to 72 if sequential search is used; 2, 5, 7, 9, 11, 17, 18, 21, 28, 30, 45, 54, 65, 69, 72. Also draw the binary tree. 5. What is the funtion of a multiplexor? Draw a multiplexor with 2^3 input lines and 1 output. How will you select the 4th input line? 6. What is the funtion of a decoder? Draw a 3 to 2^3 decoder circuit. What will happen if the binary values on input line are 101? 7. What is the maximum value(decimal) that can be represented using 5 bits of binary number?

1. To represent -29.3125 in the binary system using 16 bits, we allocate 9 bits for the mantissa, 1 bit for the sign of the number, 5 bits for the exponent, and 1 bit for the sign of the exponent.

First, let’s convert the absolute value of 29.3125 to binary. The integer part is 29, so we have:

29 = 11101

Next, let’s convert the fractional part, 0.3125, to binary. To do this, we repeatedly multiply the fractional part by 2 and take the integer part of the result. The binary representation is obtained by concatenating the integer parts.

0.3125 * 2 = 0.625 -> integer part: 0

0.625 * 2 = 1.25 -> integer part: 1

0.25 * 2 = 0.5 -> integer part: 0

0.5 * 2 = 1.0 -> integer part: 1

The binary representation of 0.3125 is 0.0101.

Now, we combine the binary representation of the integer part and the fractional part, and get:

29.3125 = 11101.0101

Next, we convert the integer part to scientific notation. In this case, the exponent is 4, and we have:

11101.0101 = 1.11010101 * 2^4

To represent the exponent, we add the bias, which is 15 (2^(5-1) – 1), to the exponent value. The exponent value is 4, so we get:

4 + 15 = 19

Convert the exponent to binary:

19 = 10011

Now, we need to determine the sign of the number, which is negative in this case. The sign bit is 1.

Finally, we have:

-29.3125 = 1 10011 111010101

The number is represented in binary using the given 16 bits.

Note: The calculation of the binary representation of negative numbers may vary depending on the specific representation scheme used.

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