Introduction to Digital Systems: Modeling, Synthesis, and Simulation Using VHDL

PROBLEMS

2.1 What is the range of unsigned integers that can be represented by the following number of bits?

1. 8
2. 10
3. 12
4. 16
5. 32
6. 64
7. 128

2.2 How many bits are required to represent the following unsigned integers?

1. 255
2. 515
3. 1242
4. 1978
5. 2004
6. 13,996
7. 122,365
8. 8,261,987
9. 29,141,991

2.3 Convert the following unsigned binary numbers into decimal, octal, and hexadecimal numbers.

1. 0.1010
2. 0.0110
3. 101100
4. 111001
5. 11000.11
6. 11101.01
7. 01110.101
8. 10101.111
9. 10110.001
10. 11100001.1001
11. 10101001.0101

2.4 Convert the following decimal numbers into binary, octal, and hexadecimal numbers.

1. 127
2. 159
3. 789
4. 1987
5. 509.43
6. 2961.72
7. 4325.53
8. 351.827
9. 612.075

2.5 Convert the following hexadecimal numbers into binary, octal, and decimal numbers.

1. 32E.15
2. 1010.AA
3. C0DE.02
4. 11F8.99
5. CAFE.45
6. F0AE.4A
7. EEFF.99
8. 10EF.75
9. BABE.01
10. 2004.FEB

2.6 Compute the following unsigned binary arithmetic operations.

1. 1101011 + 100111
2. 1011001 + 110110
3. 1000010 − 101010
4. 1100001 − 110010
5. 011101111 + 100011010
6. 100100111 + 010110011
7. 100111000 − 011010011
8. 101100001 − 011110000

2.7 Compute the following signed binary numbers using one's-complement arithmetic operations.

1. 011101111 + 101010001
2. 101110000 + 111100101
3. 011100111 + 111010011
4. 110011000 − 110011101
5. 011110111 − 110010011
6. 101100001 − 011001100

2.8 Compute the following signed binary numbers using two's-complement arithmetic operations.

1. 110111110 + 011100011
2. 010110010 + 110011101
3. 100100110 + 010110101
4. 100100110 − 010110011
5. 100111000 − 110101101
6. 111000001 − 001110010

2.9 Compute the following signed hexadecimal ...