Objectives:

-convert numbers from decimal into binary fixed point representation. -perform binary integer multiplication and division. -perform binary floating point addition and multiplication. -convert numbers from decimal into IEEE 754 single precision floating point format. -convert numbers from IEEE 754 single precision floating point format into decimal.

Assignment Description:

1. (2 pts) Perform a multiplication of two binary numbers (multiplicand 0101 and multiplier 0101) by creating a table to show steps taken, multiplicand register value, multiplier register value and product register value for each iteration by following the steps described in the following document. (Points will be deducted if steps are not shown.)

Read this steps

You can use this table to start: Multiplication table

2. (2 pts) Perform a division of two binary numbers (divide 0010 1011 by 0011 ) by creating a table to show steps taken, quotient register value, divisor register value and remainder register value for each iteration by following the steps described in the following document. (Points will be deducted if steps are not shown.)

Read this steps

You can use this table to start: Division table

3. (2 pts) Convert -1776 _ten into a 32-bit two's complement binary number.

4. (2 pts) What decimal number does this two's complement binary number represent:

1111 1111 1111 1111 1111 1100 0110 1110 _two ?

5. (2 pts) What would the number 736.40625 _ten be in IEEE 754 single precision floating point format. You need to follow the following steps:

a). Write the above number in binary. (before normalizing it)

b). Write the above number in the normalized format.

c). Compute the biased exponent, and write it in binary.

d). Write its IEEE 754 single precision floating point format in binary, then in hex.

6. (2 pts) What would the number -1891.53125 _ten be in IEEE 754 single precision floating point format.

You need to follow the following steps:

a). Write the above number in binary. (before normalizing it)

b). Write above number in the normalized format.

c). Compute the biased exponent, and write it in binary.

d). Write its IEEE 754 single precision floating point format in binary, then in hex.

7. (2 pts) What decimal number would the IEEE 754 single precision floating point number 0xC3F2B800 (this is in hex) be? Write your final answer in scientific notation as m x 10 ^p where p is an integer.

8. (2 pts) For this problem, assume 4 bits precision. Add two binary numbers, 1.011 _two x 2 ^-7 and 10.10 _two x 2 ^-5 by showing the following steps:

Step1: The significand of the number with the lesser exponent is shifted right to match the exponent of the larger number.

Step2: Add the significands. (you can assume that you can carry all digits)

Step3: Normalize the sum, determine whether there is an overflow or an underflow.

Step4: Truncate the sum (using 4 bits precision.)

9. (2 pts) For this problem, assume 4 bits precision. Multiply binary two binary numbers, 1.011 _two x 2 ^-7 and 10.10 _two x 2 ^-5 showing the following steps:

Step1: Adding the exponent without bias.

Step2: Multiply the significands. (you can assume that you can carry all digits)

Step3: Normalize the product and check for an overflow or an underflow.

Step4: Truncate the product.

10. (2 pts) Add 3.19 _ten x 10 ⁹ to 6.28 _ten x 10 ⁸, assuming the following two different ways:

a) you have only three significant digits, first with guard (2 digits) and round digits.

b) you have only three significant digits without guard and rounding.