Ahmad Ali Ahmad Othman - Section 1 - Sheet 1

1. Which of the following are analog quantities, and which are digital?

1. Number of atoms in a sample of material -> Digital
2. Altitude of an aircraft -> Analog
3. Pressure in a bicycle tire -> Analog
4. Current through a speaker -> Analog
5. Timer setting on a microwave oven -> Digital

2. Which of the following are analog quantities, and which are digital?

1. Width of a piece of lumber -> Analog
2. The amount of time before the oven buzzer goes off -> Analog
3. The time of day displayed on a quartz watch -> Display
4. Altitude above sea level measured on a staircase -> Digital
5. Altitude above sea level measured on a ramp -> Analog

3. Convert the following binary numbers to their equivalent decimal values:

A. ${11001}_2$

$$\begin{array}{c}{11001}_2=1\ast 2^4+1\ast 2^3+0\ast 2^2+0\ast 2^1+1\ast 2^0=\\ \\ 16+8+0+0+1={25}_{10}\end{array}$$

B. ${1001.1001}_2$

$$\begin{array}{c}{1001.1001}_2=1\ast 2^3+0\ast 2^2+0\ast 2^1+1\ast 2^0+1\ast 2^{-1}+0\ast 2^{-2}+0\ast 2^{-3}+1\ast 2^{-4}=\\ \\ 8+0+0+1+0.5000+0+0+0.0625={9.5625}_{10}\end{array}$$

C. $010011011001.1011{00}_2$

$$\begin{array}{c}{010011011001.10110}_2=1\ast 2^{10}+0\ast 2^9+0\ast 2^8+1\ast 2^7+1\ast 2^6+0\ast 2^5+1\ast 2^4+1\ast 2^3\\ +0\ast 2^2+0\ast 2^1+1\ast 2^0+1\ast 2^{-1}+0\ast 2^{-2}+1\ast 2^{-3}+1\ast 2^{-4}+0\ast 2^{-5}+0\ast 2^{-6}=\\ 1024+0+0+128+64+0+16+8+0+0+1\\ +0.500000+0+0.125000+0.062500+0+0={1241.6875}_{10}\end{array}$$

4. Convert the following binary numbers to decimal.

A. ${100112}_2$

$$\begin{array}{c}{10011}_2=1\ast 2^4+0\ast 2^3+0\ast 2^2+1\ast 2^1+1\ast 2^0=\\ \\ 16+0+0+2+1={19}_{10}\end{array}$$

(b) ${1100.0101}_2$

$$\begin{array}{c}{1100.0101}_2=1\ast 2^3+1\ast 2^2+0\ast 2^1+0\ast 2^0+0\ast 2^{-1}+1\ast 2^{-2}+0\ast 2^{-3}+1\ast 2^{-4}=\\ \\ 8+4+0+0+0+0.2500+0+0.0625={12.3125}_{10}\end{array}$$

C. $010011100100.1001{00}_2$

$$\begin{array}{c}{10011100100.10010}_2=1\ast 2^{10}+0\ast 2^9+0\ast 2^8+1\ast 2^7+1\ast 2^6+1\ast 2^5+0\ast 2^4+0\ast 2^3+1\ast 2^2+0\ast 2^1+0\ast 2^0\\ \\ +1\ast 2^{-1}+0\ast 2^{-2}+0\ast 2^{-3}+1\ast 2^{-4}+0\ast 2^{-5}=\\ \\ 1024+0+0+128+64+32+0+0+4+0+0+0.5000+0+0+0.0625+0={1252.5625}_{10}\end{array}$$

5. Using three bits, show the binary counting sequence from $000$ to $111$.

Decimal	Binary
0	000
1	001
2	010
3	011
4	100
5	101
6	110
7	111

6. Using six bits, show the binary counting sequence from $000000$ to $111111$.

Decimal	Binary	Decimal	Binary
0	000000	32	100000
1	000001	33	100001
2	000010	34	100010
3	000011	35	100011
4	000100	36	100100
5	000101	37	100101
6	000110	38	100110
7	000111	39	100111
8	001000	40	101000
9	001001	41	101001
10	001010	42	101010
11	001011	43	101011
12	001100	44	101100
13	001101	45	101101
14	001110	46	101110
15	001111	47	101111
16	010000	48	110000
17	010001	49	110001
18	010010	50	110010
19	010011	51	110011
20	010100	52	110100
21	010101	53	110101
22	010110	54	110110
23	010111	55	110111
24	011000	56	111000
25	011001	57	111001
26	011010	58	111010
27	011011	59	111011
28	011100	60	111100
29	011101	61	111101
30	011110	62	111110
31	011111	63	111111

7. What is the maximum number that we can count up to using 10 bits?

General rule: $2^{bits}-1$

$2^{10}-1=1023$

8. What is the maximum number that we can count up to using 14 bits?

$2^{14}-1=16383$

9. How many bits are needed to count up to a maximum of 511?

General rule: $\lceil {\log }_2(max)\rceil$ -> Ceil the log2 of the maximum.

$2^n-1=511,2^n=512,n=9$ or ${\log }_2(512)=9$

10. How many bits are needed to count up to a maximum of 63?

$2^n-1=63,2^n=64,n=6$ or ${\log }_2(64)=6$

11. Draw the timing diagram for a digital signal that continuously alternates between 0.2 V (binary 0) for 2 ms and 4.4 V (binary 1) for 4 ms.

12. Draw the timing diagram for a signal that alternates between 0.3 V (binary 0) for 5 ms and 3.9 V (binary 1) for 2 ms.

13. Suppose that the decimal integer values from 0 to 15 are to be transmitted in binary.

0. Numbers $0$ to $15$ are represented by 4 bits ($2^4=16$).
1. How many lines will be needed if parallel representation is used?
   • Parallel representation sends all bits simultaneously (at the same time), each on its own separate line.
   • That means it would use 4 Lines.
2. How many will be needed if serial representation is used?
   • Serial representation sends all bits sequentially one after the other, using a single line.
   • It would use 1 Line.

14. How is a microprocessor different from a microcomputer?

Microprocessor

• A microprocessor is a single processor core that fetches, decodes, and executes instructions.
• It requires external memory (ROM/RAM), a memory decoder, an oscillator, and I/O ports to form a complete microcomputer.
• Handles arithmetic, logic, and control operations — cannot operate alone.

Microcomputer

• A complete computer system built around a microprocessor.
• Consists of the microprocessor + memory (RAM/ROM) + I/O ports + storage + power supply, etc.
• Fully functional — capable of running programs and performing tasks independently.

15. How is a microcontroller different from a microcomputer?

Microcontroller

• A microcontroller is a compact system-on-chip (SoC) with an integrated CPU, memory (RAM, ROM), and programmable I/O peripherals, designed for specific tasks.
• Used for dedicated control tasks in embedded systems (e.g., washing machines, sensors, robotics).
• Optimized for control and efficiency, not high-speed computing.

Microcomputer

• A complete general-purpose computing system that may use a microprocessor or microcontroller as its CPU.
• Used for general-purpose computing (e.g., personal computers, workstations).
• Optimized for flexibility and processing power.