Question

1. Convert the following into the number systems specified: (a) 1101111011001? to octal and hexadecimal forms. [3 + 3 = 6 marks] (b) 3B4E5?? to denary and binary forms. [3 + 3 = 6 marks] 2. Add the binary numbers, working in binary. Express the answer as an 8-bit number, clearly showing any carry bits. 11011110? + 01101101? [5 marks] 3. Follow the scenario and instructions clearly, and state the values as an exact value, or, correct to 2 decimal places accuracy: (a) Given 2 complex numbers Z?, Z? as: Z? = 4 – 5j, Z? = –2 – 3j Find: Z = 3Z? + 2Z? in Cartesian form a + bj. [4 marks] (b) The current I in an a.c. circuit is given by I = j(0.5–2j) / (7+5j) Find the current I in polar form r??. [6 marks] 4. Convert z = –2 + j to polar form and find z? using De Moivre's theorem. Plot z and z? on an Argand diagram. [9 marks] 5. The total impedance of two impedances connected in parallel is given by 1/Z = 1/Z? + 1/Z? where Z is the total impedance and Z? = 4 + 2j and Z? = 2 – 3j are the branch impedances. Determine the current and its phase angle relative to a 110V supply voltage. [10 marks]

          1. Convert the following into the number systems specified:
(a) 1101111011001? to octal and hexadecimal forms.
[3 + 3 = 6 marks]
(b) 3B4E5?? to denary and binary forms.
[3 + 3 = 6 marks]
2. Add the binary numbers, working in binary. Express the answer as an 8-bit number, clearly showing any carry bits.
11011110? + 01101101?
[5 marks]
3. Follow the scenario and instructions clearly, and state the values as an exact value, or, correct to 2 decimal places accuracy:
(a) Given 2 complex numbers Z?, Z? as:
Z? = 4 – 5j, Z? = –2 – 3j
Find: Z = 3Z? + 2Z? in Cartesian form a + bj.
[4 marks]
(b) The current I in an a.c. circuit is given by I = j(0.5–2j) / (7+5j)
Find the current I in polar form r??.
[6 marks]
4. Convert z = –2 + j to polar form and find z? using De Moivre's theorem. Plot z and z? on an Argand diagram.
[9 marks]
5. The total impedance of two impedances connected in parallel is given by
1/Z = 1/Z? + 1/Z?
where Z is the total impedance and Z? = 4 + 2j and Z? = 2 – 3j are the branch impedances.
Determine the current and its phase angle relative to a 110V supply voltage.
[10 marks]

1. Convert the following into the number systems specified:
(a) 1101111011001? to octal and hexadecimal forms.
[3 + 3 = 6 marks]
(b) 3B4E5?? to denary and binary forms.
[3 + 3 = 6 marks]
2. Add the binary numbers, working in binary. Express the answer as an 8-bit number, clearly showing any carry bits.
11011110? + 01101101?
[5 marks]
3. Follow the scenario and instructions clearly, and state the values as an exact value, or, correct to 2 decimal places accuracy:
(a) Given 2 complex numbers Z?, Z? as:
Z? = 4 – 5j, Z? = –2 – 3j
Find: Z = 3Z? + 2Z? in Cartesian form a + bj.
[4 marks]
(b) The current I in an a.c. circuit is given by I = j(0.5–2j) / (7+5j)
Find the current I in polar form r??.
[6 marks]
4. Convert z = –2 + j to polar form and find z? using De Moivre's theorem. Plot z and z? on an Argand diagram.
[9 marks]
5. The total impedance of two impedances connected in parallel is given by
1/Z = 1/Z? + 1/Z?
where Z is the total impedance and Z? = 4 + 2j and Z? = 2 – 3j are the branch impedances.
Determine the current and its phase angle relative to a 110V supply voltage.
[10 marks]

Added by Laura B.

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