1. Translate the negative decimal number -12*2²⁰ to a 8-digit hexadecimal number in 2's complement.

Answers = 0x _____________________ (Exactly 8 hex digits. Letter digits have to be uppercase.)

2. Convert the negative decimal -110 to an 8-bit binary number in 2's complement.

(The answer has be to exactly 8 binary bits xxxxxxxx.)

Hints: Convert 110₁₀ to a binary number and then take its 2's complement.

3. Convert the following in decimal to binary fraction in the format of x.xxxxxx. (1 bit before the point and exactly 6 bits after.)

1/3 =

1/4 =

1/8=

1/16=

4. What is binary representation of value -9₁₀ in 4 bit 2's complement form?

Group of answer choices

1001

0111

Not possible to convert

1000

5. Match the following decimal numbers to binary using 6-bit 2's complement representation.

-16₁₀ 13₁₀ -3₁₀ -10₁₀ 26₁₀ -31₁₀

-16

[ Choose ] 110110 011010 100001 111101 001101 110000 None is a correct answer

13

[ Choose ] 110110 011010 100001 111101 001101 110000 None is a correct answer

-3

[ Choose ] 110110 011010 100001 111101 001101 110000 None is a correct answer

-10

[ Choose ] 110110 011010 100001 111101 001101 110000 None is a correct answer

26

[ Choose ] 110110 011010 100001 111101 001101 110000 None is a correct answer

-31

[ Choose ] 110110 011010 100001 111101 001101 110000 None is a correct answer

6. Suppose we can use at most 6 binary bits in the fraction.

Convert 4/3 in decimal to a binary fraction in the form of x.xxxxxx.

7. Numerical range of 16-bit word.in 2's complement.

Suppose we had a 16-bit word. What are the smallest and largest integer that can be represented in 2's complement?

a) -2¹⁵ and 2¹⁵ -1

b) -2^-15 and 2¹⁵ -1

c) 2^-16 and 2¹⁶

d) -2^-16 and 2¹⁶ -1

Group of answer choices

a

b

c

d

None is a correct answer.

8.

Numerical range of unsigned numbers

Suppose we had a 20-bit word. What are the smallest and the largest "unsigned" integer that can be represented?

a) 0 and 2¹⁹

b) 0 and 2¹⁹ + 1

c) 2^-20 and 2^{19 -} 1

d) 0 and 2²⁰

e) 2^-20 and 2²⁰ + 1

f) 0 and 2²⁰ - 1

Group of answer choices

a

b

c

d

e

f

None is a correct answer.