Assume that the 8-bit input word is 11001110 a) Calculate the check bits for hamming code. b) If when the data is read from memory the value 01001110 is send then recalculate the check bits for this value. c) Find the syndrome word (compare the check bits found in a and b). What does it show? Explain.

[4.1] Consider the number -1.36875 x 10¹ as the dividend and 5.625 x 10¹ as the divisor. a. Find their binary representation. b. Normalize the results that you got it in (A) and put them in the 8-bit quarter- precision format (1 for sign bit, 2 for exponent, and 5 for fraction). c. Implement the division and show all the steps of the division to results that you got it in (B). Show if there is an overflow or underflow by assuming that there is a guard bit, a round bit, and a sticky bit.

Kindly answer the following questions. j. The one thing that causes the most trouble with 2's complement numbers is the special case of the negative number which consists of a 1 followed by all 0's (1000 ... 000). If this number is n bits long, what number does it represent and why? (It is not negative zero.) a. Represent 187 in BCD code, excess-3 code, 6-3-1-1 code, and 2-out-of-5 code.

Perform the following additions. Assume that all numbers are in 8-bit 2’scomplement notation. State the carry-in and carry-out, whether overflow or not,and if the result is correct. 10011001 +10111011    Perform the following subtractions. Assume that all numbers are in 2’scomplement notation. State the carry-in and carry-out, whether overflow or not,and if the result is correct. 11101101 – 00101010

8.  Add the following two 8-bit binary numbers, producing an 8-bit result. Indicate the status of the carry and overflow bits at the end of the addition by circling the appropriate choices. The space in between is only for readability.    1111 0010 + 1101 0110    -----------   Overflow?       Yes    or    No Carry?       Yes   or    No

1. Generate the Hamming-code for the following 12-bit data string : 1 0 1 0 1 1 0 1 1 1 0 1 Show that the generated binary string does not have any errors.

- In a codeword, we add two redundant bits to each 8-bit data word. Find the following: Number of valid codewords , Number of invalid codewords.  - If we want to be able to detect 2-bit errors, what should be the minimum Hamming distance? - In CRC, if the dataword is 5 bits and the codeword is 8 bits, how many 0s need to be added to the dataword to make the dividend? What is the size of the remainder? What is the size of the divisor?

The following is a string of ASCII characters whose bit patterns have been converted intohexadecimal for compactness: 73 F4 E5 76 E5 4A EF 62 73. Of the eight bits in each pairof digits, the leftmost is a parity bit. The remaining bits are the ASCII code.(a) Convert the string to bit form and decode the ASCII.(b) Determine the parity used: odd or even?

7. Add the following two 8-bit binary numbers, producing an 8-bit result. Indicate the status of the carry and overflow bits at the end of the addition by circling the appropriate choices. The space in between is only for readability.    1101 0110 + 1001 0111 --------------   Overflow?       Yes    or    No Carry?       Yes   or     No

In single precision (IEEE-754 standard), 8 bits are used for storing the exponent (the bias is 127), and 23 bits are used for storing the mantissa.  (a) What are the smallest and the largest positive numbers that can be stored in single precision? (b) What is the smallest value of the mantissa that can be stored?