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 * * * 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:
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:
( )2
(26.24)8
(a) ( )2= =
(b) (26.24)8 = 2* /8 + 4/64 =
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 =
Convert from decimal to binary.
Convert from binary to decimal.
Compare results.
By Nora Alaqeel

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

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

12. Exercises
Q 1.15 find 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
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)
> 6590 (9’s comp) -> 6591 (10s comp)
6428 – 3409 = = 3019
By Nora Alaqeel

15. Exercises
Q 1.19 the following decimal numbers are shown in sign-magnitude form: +9,286 and 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)
> ; >
> ; >
(c) (-9286) + (+801) = =
By Nora Alaqeel

16. Exercises Q 1.22 Convert decimal 8,723 to BCD.
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:
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. G
(dot)
(space) B o l e
By Nora Alaqeel

20. Exercises
Q 1.29 Decode the following ASCII code:
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