BEEE102L – Basic Electrical and Electronics Engineering
Solve to Learn – Worksheet 9 – Graded
Topic: Digital Circuits
(Number Systems, Binary Arithmetic, Simplification of Boolean Functions)
1. How many bits per word are needed to represent the decimal integers (n bits can
represent 2 different combinations)
a. 0 though 127
b. 0 through 500
c. 0 through 1000
2. What range of decimal integers can be represented by
a. 4-bit binary numbers
b. 4-digit octal number
c. 4-digit hexadecimal number
3. Convert the binary numbers to decimal, octal and hexadecimal
a. 10101.001
b. 1111.11
4. Express the decimal numbers in binary form and binary coded decimal form
a. 11.75
b. 67.375
5. Convert the following numbers to decimal and octal
a. (𝐸𝐵4.5)
b. (𝐵𝐴. 𝐶)
6. Convert the following numbers to binary, hexadecimal and decimal forms
a. (123.5)
b. (644.2)
7. Perform the following operations using 8-bit signed two’s compliment arithmetic
a. (43) - (45)
b. (59) - (34)
c. (−27) + (15)
d. (−33) – (−45)
8. Draw a circuit to realize the following Boolean expression using AND, OR and NOT
gates F=𝐴𝐵 𝐶 + 𝐴𝐵𝐶̅ + 𝐴̅𝐵𝐶. Find the complement of the function and realize the
circuit again.
9. Draw the truth table for the Boolean expression and express it as sum of products (SOP)
and product of sums (POS) F=A+ 𝐴𝐵 𝐶
10. Construct Karnaugh map for the function and find the minimum SOP and minimum
POS expressions.
a. F=∑ 𝑚(0, 2, 4, 6, 7)
b. F=∏ 𝑀(1, 2, 3, 5)