1. Write IEEE floating point representation of the following decimal number 3.75

3.75 = 011.112 = 1.1112 = 1.111 x 2^1 exp – 127 = 1 exp = 128 fraction = 11100000000000000000000 3.75 = 01000000011100000000000000000000 #

2. Write IEEE floating point representation of the following decimal number -55 23/64

-55 23/64 = -55.359375 011011.010111 = 1.1011010111 x 2^5 exp - 127 = nilai anjakan exp -127 = 5 exp = 5 + 127 = 132 = 10000100 fraction = 10111010111000000000000 -55 23/64 = -ve = 1 = 110000100101110111000000000000 #

3. Write IEEE floating point representation of the following decimal number 64000

64000 = 111110100000000 = 1.11110100000000 = 1.1111010000000 x 2^15 exp - 127 = nilai anjakan exp = 15 + 127 exp = 142 = 10001110 sign = 0 (+ve) =01000111011110100000000000000000 #

4. Write the decimal equivalent for this IEEE floating point number 01000000000000000000000000000000

1. Fraction = 0 2. Sign = 0 3. exp = 128 = 127 + 1 exp - 127 = 1 4. N = (-1^0) * (1.0) * (2^1) = 1 * 1 * 2 = 2 #

5. Write the decimal equivalent for this IEEE floating point number 11000001100010000000000000000000

1.Fraction = 0001 0000 0000 0000 0000 000 = 0.0625 2. Sign = 1 3. exp = 131 = 127 + 4 exp - 127 = 4 4. N = (-1^1) * (1.0625) * (2 ^ 4) = -1 * 1.0625 * 16 = -17 #

6. Write the decimal equivalent for this IEEE floating point number 01111111100000000000000000000000

1. Sign = 0 2. Fraction = 0 3. exp = 255 4. N = +∞ #

7. Write the decimal equivalent for this IEEE floating point number 11000000010010000000000000000000

1. Sign = 1 2. Fraction = 1001 0000 0000 0000 0000 000 = 0.5625 3. exp = 128 = 127 + 1 exp - 127 = 1 4. N = (-1^1) * (1.5625) * (2^1) = -1 * 1.5625 * 2 = -3.125 #

8. Convert the following unsigned binary number 1101000110101111 to hexadecimal.

1101 0001 1010 1111 = 13 1 10 15 = D 1 A F = D1AF

9. Convert the following unsigned binary number 0011111 to hexadecimal.

001 1111 = 0001 1111 = 1 F = 1F

10. Convert the following unsigned binary number 1 to hexadecimal.

1 = 0001 = 1

11. Convert the following unsigned binary number 1110110110110010 to hexadecimal.

1110 1101 1011 0010 = 14 13 11 2 = E D B 2 = EDB2

12. Convert the following hexadecimal number x10 to binary.

1016 = 1 0 = 0001 0000 = 00010000

13. Convert the following hexadecimal number x801 to binary.

x801 = 8 0 1 = 1000 0000 0001

14. Convert the following hexadecimal number xF731 to binary.

xF731 = F 7 3 1 = 1111 0111 0011 0001 = 1111011100110001

15. Convert the following hexadecimal number x0F1E2D to binary.

x0F1E2D = 0 F 1 E 2 D = 0000 1111 0001 1110 0010 1101 = 000011110001111000101101

16. Convert the following hexadecimal number xBCAD to binary.

xBCAD = B C A D = 1011 1100 1010 1101 = 1011110010101101

17. Convert the following hexadecimal representation of 2’s complement binary number xF0 to decimal number.

xF0 = F 0 = 1111 0000 = 11110000 = 00001111 + 1 ----------------- = 00010000 = -16 #

18. Convert the following hexadecimal representation of 2’s complement binary number x7FF to decimal number.

x7FF 2048 1024 512 256 128 64 32 16 8 4 2 1 0 1 1 1 1 1 1 1 1 1 1 1 = 7 F F = 0111 1111 1111 = (0x10^11) + (1x10^10) + (1x10^9) + (1x10^8) + (1x10^7) + (1x10^6) + (1x10^5) + (1x10^4) + (1x10^3) + (1x10^2) + (1x10^1) + (1x10^0) = 0 + 1024 + 512 + 256 + 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 2047 #

19. Convert the following hexadecimal representation of 2’s complement binary number x16 to decimal number.

x16 128 64 32 16 8 4 2 1 0 0 0 1 0 1 1 0 = 1 6 = 0001 0110 = (1x10^4) + (1x10^2) + (1x10^1) = 16 + 4 + 2 = 22 #

20. Convert the following hexadecimal representation of 2’s complement binary number x8000 to decimal number.

x8000 32768 16384 8182 4096 2048 1024 512 256 128 64 32 16 8 4 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 = 1000 0000 0000 0000 = 0111 1111 1111 1111 + 1 --------------------------------- = 1000 0000 0000 0000 =(1x10^15) + (0x10^14) + (0x10^13) + (0x10^12) + (0x10^11) + (0x10^10) + (0x10^9) + (0x10^8) + (0x10^7) + (0x10^6) + (0x10^5) + (0x10^4) + (0x10^3) + (0x10^2) + (0x10^1) + (0x10^0) = 32768 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 = 32768 #

21. Convert the following decimal number 256 to hexadecimal representation of 2’s complement number.

256 256| 2 b 0 128| 2 b 0 64 | 2 b 0 32 | 2 b 0 16 | 2 b 0 8 | 2 b 0 4 | 2 b 0 2 | 2 b 0 1 1|0000|0000 0001 0000 0000 100

22. Convert the following decimal number 111 to hexadecimal representation of 2’s complement number.

111 = 110111

23.Convert the following decimal number -44 to hexadecimal representation of 2’s complement number.

44 = 101100 = 0010 1100 = 1101 0011 = 1101 0100 = D4 #

24. Perform the following addition x025B + x26DE. The corresponding 16-bit binary number is in 2’s complement notation. Provide your answer in hexadecimal.

x025B + x26DE 025B + 26DE ------------- = 2939 #

25. Perform the following addition x7D96 + xF0A0. The corresponding 16-bit binary number is in 2’s complement notation. Provide your answer in hexadecimal.

x7D96 + xF0A0 7D96 + F0A0 -------------- = 16E36 #

26. Perform the following addition xA397 + xA35D. The corresponding 16-bit binary number is in 2’s complement notation. Provide your answer in hexadecimal.

xA397 + xA35D A397 + A35D ------------- = 146F4 #

27. Perform the following addition x7D96 + x7412. The corresponding 16-bit binary number is in 2’s complement notation. Provide your answer in hexadecimal.

x7D96 + x7412 7D96 + 7412 -------------- = F1A8 #

28. What is the hexadecimal representation of 675.625?

675.625 675 = 0010 1010 0011 0.625 = 0.1010 0010 1010 0011 . 1010 1.0101000111010 x 2^9 exp - 127 = 9 exp = 136 = 10001000 fraction = 0 1010 0011 1010 0000 0000 00 sign = 0 0100 | 0100 | 0010 | 1000 | 1110 | 1000 | 0000 | 0000 4 4 2 8 E 8 0 0 4428E800

29. Answer the following arithmetic operation in binary 01010111 + 11010111

01010111 + 11010111 --------------------- = 00101110 asas 2 #

30. Answer the following arithmetic operation in binary 1111 + 100001111 + 0111

111111111 + 100001111 =1100001110 1100001110 +0111=1100010101 #

31. Find out the answer for the following arithmetic operation x3F0 + 12348. State your answer in any number system given in the question.

convert to binary 3F0=0011 1111 0000 1234

32. Find out the answer for the following arithmetic operation 2345 + 1234. State your answer in any number system given in the question.

234 (