Homeworks 관련

• hw01
  • 2.1
  • 2.2
  • 2.3
  • 2.4
  • 2.5
  • 2.6
  • 2.7
  • 2.8
  • 2.9
• 2.10
• 2.11
• 2.12
• 2.13
• 2.14
• 2.15
• 2.16
• 2.17
• 2.18
• 2.19
• 2.20
• 2.21
• 2.22
• 2.23
• 2.24
• 2.25
• 2.26
• 2.27
• 2.28
• 2.29
• 2.30
• 2.31
• 2.32
• 2.33

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hw01

2.1

Give the entire count sequence of binary patterns for 3-bit unsigned integers.

2.2

What is the decimal value represented by the 8-bit binary number $11001001.0101_2$ when interpreted as:

(a) an unsigned number?

(b) A 2's-complement number?

2.3

What is the decimal value represented by the binary number $10001101_2$ when interpreted as:

(a) an sign + magnitude number?

(b) A 2's-complement number?

2.4

Use polynomial evaluation to:

(a) Convert $$101101_2$$ to base 10

(b) Convert $$\text{DEAF}_{16}$$ to base 10.

(c) Convert $$0.324_7$$ to base 10.

2.5

Use repeated division to:

(a) Convert $$150_{10}$$ to base 2.

(b) Convert $$1500_{10}$$ to base 16.

(c) Convert $$400_{10}$$ to base 7.

2.6

Use repeated multiplication to:

(a) Convert $$0.9_{10}$$ to base 2.

(b) Convert $$0.9_{10}$$ to base 16.

(c) Convert $$0.9_{10}$$ to base 3.

2.7

Use shortcuts based on power relationships to:

(a) Convert $\text{ACE}5_{16}$ to base 2.

(b) Convert $\text{FACE}_{16}$ to base 8.

(c) Convert $1011.0111_2$ to base 8.

(d) Convert $232.1_4$ to base 8.

(e) Convert $$17.6_9$$ to base 3.

2.8

Perform the indicated conversions:

(a) Convert $$\text{FA}.\text{CE}_{16}$$ to base 2 (binary).

(b) Convert $$101011.01101_2$$ to base 16 (hexadecimal).

(c) Convert $$56.23_{10}$$ to base 2 (binary).

(d) Convert $$11011.01101_2$$ to base 10 (decimal).

(e) Convert $$12.34_5$$ to base 7.

2.9

Convert the decimal number $$-37.1_{10}$$ to 16-bit 2's-complement binary, with 8 bits of integer part and 8 bits of fractional part.

2.10

What is the 2's-complement 8-bit representation of $$-100_{10}$$?

2.11

Give the 2's-complement 8-bit representation of $$-7.7_{10}$$, with the binary point in the middle (e.g. $$bbbb.bbbb$$).

2.12

For each of the following 2's-complement numbers, give the corresponding 8-bit representation of the negative of its value:

(a) $$01010101.$$

(b) $$10101010.$$

(c) $$1000.0001$$

(d) $$0111.1110$$

2.13

Consider a 2's complement number represented by $$n$$ bits, with the binary point placed between the two most significant bits (e.g., $$b.bb\cdots{b}$$).

(a) Give an algebraic expression in terms of $$n$$ for the positive value that has the smallest nonzero magnitude.

(b) Give the binary representation of (a). where $$n$$ is 8.

(c) Give an algebraic expression in terms of $$n$$ for the negative value that has the smallest nonzero magnitude.

(d) Give the binary representation of (c). where $$n$$ is 8.

2.14

Give the 32-bit binary representation of the floating-point value $$-25.1$$:

2.15

The ASCII code for the symbol “0” is $$30_{16}$$. Use this fact to determine the hex constants that would be stored in memory, starting at $$N$$, for the $$C$$ character string “12345”:

2.16

Perform the indicated addition on the following 4-bit operands, filling in all the indicated fields:

2.17

Perform the indicated subtraction on the following 4-bit operands, filling in all the indicated fields:

2.18

If the operands are unsigned, then does an overflow occur:

(a) In problem 16?

(b) In problem 17?

2.19

If the operands are signed, then does an overflow occur:

(a) In problem 16?

(b) In problem 17?

2.20

Find the indicated sum of the following signed 8-bit 2's-complement numbers and the indicate which cause an arithmetic overflow to occur:

(a)

$$\begin{matrix} &\:00111110\\ +&\:01101100\\\hline \end{matrix}$$

(b)

$$\begin{matrix} &\:01011011\\ +&\:10110101\\\hline \end{matrix}$$

(c)

$$\begin{matrix} &\:11101011\\ +&\:11110100\\\hline \end{matrix}$$

2.21

Find the indicated difference of the following signed 8-bit 2's-complement numbers and the indicate which cause an arithmetic overflow to occur:

(a)

$$\begin{matrix} &\:00101100\\ -&\:010110101\\\hline \end{matrix}$$

(b)

$$\begin{matrix} &\:00101110\\ -&\:11101011\\\hline \end{matrix}$$

(c)

$$\begin{matrix} &\:11000100\\ -&\:10101101\\\hline \end{matrix}$$

2.22

Assume that the C assignment statement “s=a+b” has just been executed, where all variables are declared as signed ints. Write a C expression that is true if and only if the addition results in an overflow.

2.23

Repeat problem 22 for the C assignment statement “s=a-b”.

2.24

What is the most positive decimal value of a 6-bit 2's-complement number?

2.25

What is the most negative decimal value of a 6-bit 2's-complement number?

2.26

What is the minimum decimal value of a 6-bit unsigned number?

2.27

What is the maximum decimal value of a 6-bit unsigned number?

2.28

The exact binary representation of one-sixth ($$\tfrac{1}{6}$$) requires an infinite number of digits. Truncating it (discarding extra bits) to make it fit within a fixed-precision representation creates a representational error. What is the absolute error that results from storing one-sixth without rounding using $$8$$ fractional bits?

2.29

Overflow is impossible when subtracting one unsigned number from another. [T/F]

2.30

Overflow is impossible when subtracting two signed operands of the same sign. [T/F]

2.31

There are two representations of zero in 2's complement. [T/F]

2.32

If rollover occurs when incrementing an integer, there is an overflow. [T/F]

2.33

In 2's complement, the absolute values of full-scale negative and full-scale positive are identical. [T/F]