Digital Circuits (2025) – Tutorial Two
Q1. Consider the following numbers:
• Nineteen
• Thirty-three
• Sixty-nine
• Four hundred
Represent these numbers using the unsigned binary system.
Q2. Consider the unsigned binary number 10101001.
• Represent this number in decimal.
• Represent this number in hexadecimal.
Q3. Consider a four-bit unsigned binary system. Perform the following
operations:
0011 × 0011,
0011 × 0101,
0111 × 0010
Q4. Represent the number one hundred in numeric systems that use the
following bases:
9, 7, 5, 3, 2
Q5. Consider numeric systems with bases 3, 5, 7, and 9. Let each system
use three digits.
How many patterns can be represented by each of these systems?
Q6. Consider the following numeric systems:
• Eight-bit unsigned binary system
• Sixteen-bit unsigned binary system
• Thirty-two-bit unsigned binary system
• Sixty-four-bit unsigned binary system
1
Determine the range of values that can be represented by each of these
systems.
Q7. Consider the following set {0, 16, 32, 64}.
How many bits are needed to represent the elements of this set using binary patterns?
Q8. Convert the following decimal numbers to binary and hexadecimal
systems:
57, 142, 255
Q9. Convert the following decimal numbers to octal and hexadecimal
systems:
73, 200, 512
Q10. Convert the following floating-point decimal numbers to binary:
10.875,
7.625,
15.3125
Q11. Convert the following binary floating-point numbers to decimal:
1010.111,
111.101,
2
1111.0101