Problem 1
Given our discussion of positional numbering systems in Section 4.2.1, see whether you can determine the decimal value of the following numbers: a. 133 (base 4) b. 367 (base 8 , also called octal) c. 1BA (base 16, also called hexadecimal. B is the digit that represents 11 ; \(\mathrm{A}\) is the digit that represents \(10 .)\)
Problem 3
Determine the decimal value of the following unsigned binary numbers: a. 11000 b. 110001 c. 1111111 d. 1000000000
Problem 4
Using 8 bits, what is the unsigned binary representation of each of the following values: a. 23 b. 55 c. 275 Did anything unusual happen when determining the correct answer to Part c?
Problem 5
Assume that the following 10 -bit numbers represent signed integers using sign/ magnitude notation. The sign is the leftmost bit and the remaining 9 bits represent the magnitude. What is the decimal value of each? a. 1000110001 b. 0110011000 c. 1000000001 d. 1000000000
Problem 6
Give the 8-bit sign/magnitude representation of each of the following decimal values: a. \(+71\) b. \(-1\) c. \(-81\)
Problem 7
Assume that you tried to store the signed integer value \(-200\) using an 8-bit sign/ magnitude representation. What happened? What type of error does this represent?
Problem 8
Assume that we use 10 bits to represent signed integers, using \(\operatorname{sign} /\) magnitude notation. What are the largest (in absolute value) positive and negative numbers that can be represented on our system?
Problem 9
Show the step-by-step addition of the following two 10-bit unsigned binary values, including showing the carry bit to each successive column: \begin{tabular}{r} 0011100011 \\ \(+0001101110\) \\ \hline \end{tabular}
Problem 12
In Exercises 10 and 11, we used 16 bits to represent decimal numbers, allocating 10 bits for the mantissa and 6 bits for the exponent. What would be the impact on our representation if we still used 16 bits for each number but instead allocated 12 bits for the mantissa and 4 bits for the exponent?
Problem 14
How many binary digits would it take to represent the following phrase in ASCll code? In 16-bit Unicode? (Do not include the " " marks.) "Invitation to Computer Science"
