JEE 160 Exam 1

1. Convert (174.78125)10 to binary, octal, and hexadecimal (10 points). 

174/2 = 87 r0        0.78125 * 2 = 1.5625
87/2  = 43 r1        0.5625  * 2 = 1.125
43/2  = 21 r1        0.125   * 2 = 0.25
21/2  = 10 r1        0.25    * 2 = 0.5
10/2  =  5 r0        0.5     * 2 = 1.0
5/2   =  2 r1
2/2   =  1 r0
1/2   =  0 r1

(10101110.11001)2
(256.62)8
(AE.C8)16

The circuit shown below is used in problems 2 and 3.

2. Draw the equivalent circuit using NAND gates and inverters as necessary. (10 points)

3. Derive the minimized sum-of-products or product-of-sums equation. (15 points)

4. Use the design procedure to design a circuit to convert an 'X' code count to normal binary. The 'X' code counting sequence from 0 to 15 is as follows: 0000, 0101, 1111, 1010, 0001, 0111, 1110, 1000, 0011, 0110, 1100, 1001, 0010, 0100, 1101, 1011. (25 points)

5. Implement the following Boolean function with an 8-to-1 multiplexer and one inverter. (10 points)
F(A,B,C,D) = SUM m(2,5,6,7,12,13,14)

6. Using Full Adders and the minimum amount of additional logic, design a 4 bit binary subtraction circuit. Both input numbers are in signed 2's complement form. Also, add circuitry to detect an overflow. (20 points)