Digital Logic Design

1. Digital Logic Design Lab 1,2 By Nora Alaqeel

2. Exercises Q 1.3 Convert the following numbers with the indicated bases to decimal: (b) (735)8 (735)8= 7 * 82+ 3 * 81+ 5 * 80= 47710 By Nora Alaqeel

3. Exercises Q 1.4 What is the largest binary number that can be expressed with 14 bits? What are the equivalent decimal and hexadecimal numbers? 14-bit binary: 11 1111 1111 1111 Decimal: 16,38310 Hexadecimal: 3FFF16 By Nora Alaqeel

4. Exercises Q 1.5 Determine the base of the numbers in each case for the following operations to be correct: (a) 14 / 2 = 5 Let b = base 14/2 = (b+4) / 2 = 5, So b=6 By Nora Alaqeel

5. Exercises Q 1.9 Express the following numbers in decimal: (10110.0101)2 (26.24)8 (a) (10110.0101)2= 16 + 4 + 2 + 0.25 + 0.0625 = 22.3125 (b) (26.24)8 = 2*8 + 6 + 2/8 + 4/64 = 22.3125 By Nora Alaqeel

6. Exercises Q 1.12 Add and Multiply the following numbers without converting them to decimal: (a) Binary numbers 1011 and 101. By Nora Alaqeel

7. Exercises (a) Binary numbers 1011 and 101. Add: Multiply: By Nora Alaqeel

8. Exercises Q 1.13 Do the following conversion problems: (b) Calculate the binary equivalent of 2/3 out of 8 places. Then convert from binary to decimal. How close is the result to 2/3 ? • 2/3 = .6666666667 • Convert from decimal to binary. • Convert from binary to decimal. • Compare results. By Nora Alaqeel

9. Exercises Convert from decimal to binary. (.6666666667)10 = (.10101010)2 By Nora Alaqeel

10. Exercises • Convert from binary to decimal. .10101010 = (1*2-1) + (1*2-3) + (1*2-5) + (1*2-7)= (1/21) + (1/23) + (1/25) + (1/27) = (1/2) + (1/8) + (1/32) + (1/128) = 0.5 + 0.125 + 0.03125 + 0.0078125 = 0.6641 By Nora Alaqeel

11. Exercises Q 1.14Obtain the 1’s and 2’s complements of the following binary numbers: (a) 10000000 1’s comp: 01111111 2’s comp: 10000000 By Nora Alaqeel

12. Exercises Q 1.15find the 9’s and 10’s complements of the following decimal numbers: (a) 52,784,630 9’s comp: 47,215,369 10’s comp: 47,215,370 By Nora Alaqeel

13. Exercises Q 1.16 Find the 16’s complements of B2FA 15’s comp: 4D05 16’s comp: 4D06 By Nora Alaqeel

14. Exercises Q 1.17 Perform subtraction on the given unsigned numbers using the 10’s complements of the subtrahend. Where the result should be negative. (a) 6428 - 3409 3409 -> 6590 (9’s comp) -> 6591 (10s comp) 6428 – 3409 = 6428 + 6591 = 3019 By Nora Alaqeel

15. Exercises Q 1.19 the following decimal numbers are shown in sign-magnitude form: +9,286 and +801. Convert them to signed-10’s complement form and perform the following operations (note that the sum is +10,627 and requires five digits and sign). (c)(-9286) + (+801) +9286 -> 009286; +801 -> 000801 -9286 -> 990714; -801 -> 999199 (c) (-9286) + (+801) = 990714 + 00801 = 991515 By Nora Alaqeel

16. Exercises Q 1.22 Convert decimal 8,723 to BCD. 8,723BCD: 1000 0111 0010 0011 By Nora Alaqeel

17. Exercises Q 1.23 Represent the unsigned decimal numbers 842 and 537 in BCD, and show the steps necessary to form their sum. Invalid BCD code By Nora Alaqeel

18. Q 1.25 Represent the decimal number 5137 in BCD: Excess-3: 0101 0001 0011 0111 1000 0100 0110 1010 By Nora Alaqeel

19. Exercises Q 1.28 Write the expression “G. Boole” in ASCII, using an eight-bit cod. Include the period and the space. Treat the leftmost bit of each character as a parity bit. Each eight-bit code should have even parity. By Nora Alaqeel

20. Exercises Q 1.29 Decode the following ASCII code: 1000010 1101001 1101100 1101100 1000111 1100001 1110100 1100101 1110011 Bill Gates By Nora Alaqeel

21. Exercises Q 1.34 List the ASCII code for the 10 decimal digits with the odd parity bit in the leftmost position. By Nora Alaqeel