EC605 Homework 1 Solved

Homework 1

1. [Combinational Logic]
Given the following truth table:

EC605 Computer Engineering Fundamentals, Fall 2021

1. a)  Write the sum-of-products formula for the truth table.
2. b)  Simplify your formula as much as you can. Show your work.
3. c)  Draw the gate-level logic circuit which corresponds to your simplified formula.

2. [Combinational Logic]

   Write the (un-simplified) formulas expression for Y and Z below:

3. [Number Represenation]
   Convert the following numbers to 8 bit signed 2’s complement binary, and to hexadecimal. Provide both answers and show your work – do not use a calculator. a) (25)10
   b) (-62)10
   c) (127)10
4. [Number Represenation]
   Convert the following numbers to decimal. Show your work – do not use a calculator. a) (6AFA)16

a) 00110110 + 01000101 ————

b) 01110101 + 11011110 ————

c) 10011101 + 10000001 ————

d) 00101101 x 00000101 ————

EC605 Computer Engineering Fundamentals, Fall 2021

2. b)  (0010 0001)2’s complement
3. c)  (1011 1001)2’s complement

5. [Floating Point Representation]
   1. a)  Convert the decimal number 63.25 to binary representation using the IEEE 754

      single precision format. Represent your answer in binary and hex, and show your

      work.

   2. b)  Convert the IEEE 754 single precision format number 0xC1300000 to decimal.

      Show your work.

6. [Binary Arithmetic]
   Perform the following operations involving 8-bit 2’s complement numbers and indicate whether arithmetic overflow occurs. Check your answers by converting to decimal sign and magnitude representation. Notice that part (d) involves multiplication.

7. [K-maps]
Simplify the following expressions using K-maps:

1. a)  F(x,y,z) = x’y’z’ + x’y’z + x’yz + xy’z’ + xy’z
2. b)  F(x,y,z) = x’y’z + x’yz + xy’z + xyz
3. c)  F(A,B,C,D) = A’B’C’D’ + AC’D’ + B’CD’ + A’BCD + BC’D
4. d)  F(w,x,y,z) = x’z + w’xy’ + w(x’y + xy’)