COSC 3332 HW1

1. Convert the following numbers from decimal to binary, assuming nine-bit twos complement binary representation.

• 35
• -256
• -1

2. Convert the following numbers from binary to decimal, assuming nine-bit twos complement binary representation.

• 0 0111 0101
• 1 0110 1010
• 1 0000 0001

3. Convert the following decimal fractions to binary with a maximum of six places to the right of the binary point:

• 25.84375
• 57.55

4. Convert the following number from binary to decimal.

• 1010000.11101
• 1010100.110111

5. Given a tiny computer that has a word size of 8 bits, what are the smallest negative numbers and the largest positive numbers that this computer can represent in Twos complement.

6. Perform the following binary multiplications, assuming unsigned integers:

• 1011 x 101
• 10011 x 1011
• 11010 x 1011

7. Perform the following binary divisions, assuming unsigned integers:

• 11111101 / 1011
• 110010101 / 1001
• 1001111100 / 1100

8. Assume we are using the simple model for floating-point representation as given in the text (the representation uses a 14-bit format, 5 bits for the exponent with a bias of 15, a normalized mantissa of 8 bits, and a single sign bit for the number):

• Show how the computer would represent the numbers 100.0 and 0.25 using this floating-point format.
• Show how the computer would add the two floating-point numbers in part a by changing one of the numbers so they are both expressed using the same power of 2.
• ) Show how the computer would represent the sum in part b using the given floating-point representation. What decimal value for the sum is the computer actually storing? Explain.

9. Decode the following ASCII message, assuming 7-bit ASCII characters and no parity: 1001010 1001111 1001000 1001110 0100000 1000100 1001111 1000101

10. Using the CRC polynomial 1101, compute the CRC code word for the information word, 01001101. Check the division performed at the receiver.