(a) What are fixed point numbers in a computer system? Why are negative fixed point numbers represented in complement form? Give examples of fixed point numbers (positive as well as negative) assuming the size of the notation to be 8 bits (including sign bit).

Perform the following arithmetic operations using signed 2’s complement 8 bit representation. (Please note that the numbers given below are in decimal notation)

i) Add –30 and –98

ii) Subtract –79 from 45

Please indicate overflow if it is occurs. Explain how have you identified the overflow?

(b) Perform the following conversion of numbers:

i) Decimal (56789123)10 to binary and hexadecimal

ii) Hexadecimal (ABCDEF0)H into Octal.

iii) ASCII string “Subject: Computer %$ Sc.” into UTF 8 string iv) Octal (345123)O into Decimal

(c) Design a circuit for the following function:

F(A, B, C, D) = ? (2,3,4, 5, 10, 11, 12, 13)

Draw the truth table. Use the Karnaugh’s map to design the circuit and draw it using AND, OR and NOT gates.

(e) Design a two bit down counter (a sequential circuit). The counter states are 11, 10, 01, 00, 11, 10, 01, 00, 11…You should show the state table, state diagram, the k-map for circuit design and logic diagram of the resultant design using D flipflop or J-K flip flop.

(f) What is floating point number? What is the difference between Single precision and double precision floating point numbers? What is a representation for Zero in IEEE 754 single precision standard. Represent (-23456.05)10 and (0.00025)10 in IEEE 754 single precision format

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