7. A pair of 7-bit floating point formats, based on the IEEE standard, is described below: (a) Format (a) has k = 3 and n = 4. The exponent bias is 3. Format (b) has k = 4 and n = 3. The exponent bias is 7. Convert the bit patterns below, given in format (a) to bit patterns in format (b). Convert exact values when possible, otherwise use the round-to-even rule. Also, write the values of each bit pattern, for the (a) and (b) formats. Write the values, in decimal, as rational numbers, or whole integers. Bits (a) Value Bits (b) Value 1 0111 000 011 0000 101 1010 110 1011 000 0011 1 (b) What is the smallest positive denormalized number in format (b)? What is the largest positive denormalized number in format (b)?

Assume that a system uses 10-bit floating-point representation based on the IEEE floating-point format, in which: . There is 1 sign bit. There are k= 6 exponent bits. The exponent bias is 31. . There are n= 3 fraction bits. ● Convert the decimal number -5.5 into the 10-bit IEEE floating point representation explained above. Write the final result in 10-bit binary format. Show your steps.

2. Assume we are using the simple model for floating-point representation as given in this book (the representation uses a 16-bit format, 5 bits for the exponent with a bias of excess-15, a normalized mantissa of 10 bits, and a single sign bit for the number): Show how the computer would represent the numbers a) +3.53125 and -3.34375 using this floating-point format. a) +3.53125 b)-0.09375

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

Are you able to differentiate between the least significant bit and the most significant bit in a given set of data?

Write down the bit pattern in the fraction assuming a fl oating point format that uses Binary Coded Decimal (base 10) numbers in the fraction instead of base 2. Assume there are 24 bits, and you do not need to normalize. Is this representation exact?

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?

1 a. If the last operation performed on a computer with an 8-bit word was an addition in which the two operands were 00000010 and 00000011, what would be the value of the following flags? ● Carry • Zero • Overflow Sign • Even Parity ● Half-Carry b. Repeat for the addition of -1 (twos complement) and +1.

6. Using IEEE 754 representation for single precision floating point, give the 32-bit binary encoding for the numbers below. Show the sign, exponent, and mantissa (significand).b. 11.2265625

Can please help with part a and b and show work