CSC 215 Exam 2 Name Fatema 1. Design a combinational circuit that converts a four-bit Gray code A, B, C, D (a binary numeral system where two successive values differ in only one bit, shown as table blow) to a bit four-binary number w, x, y, z. ABCD wxyz 0000 0000 0001 0001 0011 0010 4 0010 0011 0110 0100 4 0111 0101 g 0101 0110 6 0100 0111 1100 1000 1101 1001 1111 1010 1110 1011 1010 1100 1011 1101 b) Do the circuit (5 1001 1110 1000 1111 1x2 a) Using Karnaugh maps, obtain a minimum sum-of-products form w, x, y, and z. (20 points) 0:1 1.0 10 00 h map for W 92 92 90 2 9-21 10 O 0 0 D 0 ωχ 6.1. ド 0 1 1 1

The given function table is for an eight-bit ALU circuit with Bounded Signed Integers in Two’s Complement Representation. Modify it to represent signed 4-bit two's complement representation.

Q1: For the Karnaugh map in Figure shown below, add a 1 in the lower right cell (1010) and determine the resulting SOP expression. |x AB 8 00 OF 11 10 8 (0) 1 1 01 11 10 T C 1 1

Using a multiplexer, implement the Boolean Function F(A,B,C,D) = Sum_m(3,7,11,12,13,14,15) with select lines A,C, and D? What is the optimum size of the MUX?

1. Which of the following function is the simplest SOP expression obtained from the Karnaugh map (K- map) shown below? C' C CD AB 00 01 11 10 00 1 1 B' A' 01 1 1 11 1 1 10 1 B' D' D. D'

Consider a special purpose decoder that is called BCD to seven-segment decoder. The decoder takes a 4-bit Binary Coded Decimal (BCD) number X3 X2 X4 X0 (0-9) and produces 7 outputs a, b, c, d, e, f, and g The specification of this circuit is as follows: ⚫ The 7 outputs of the decoder are connected to LED segments as shown in the figure below. The LEDs are active low, ie, the LED emits light when it is connected to logic 0. • The decoder output is determined in a way so that the LED segments display the decimal representation of the input. For example, if the input X3 X2 X1 X0 is 0001 respectively (which is equivalent to decimal 1), the outputs a, b, c, d, e, f, and gare 1001111 showing the letter 1 on the display (remember the LEDs are active low). Decoder W- 4x7 e U Answer the following questions: a. Fill in the truth table of that decoder. Choose a good value for the output when the input is greater than decimal 9. b. Derive the simplified Boolean expressions for the outputs a, b, c,…

X = 4F(A, B, C, D) = ∑m(X, X+3, X+4, X+5, 13, 14, 15)implement the followingfunction F by using one 8-to-1 multiplexer.

A switching circuit has four inputs as shown. A and B represent the first and second bits of an unsigned binary number N1. C and D represent the first and second bits of an unsigned binary number N2. The output is to be 1 only if the product N1 x N2 is less than or equal to 3. Otherwise, the output is zero. N1 B N2 D (a) Find the minterm expansion for F. (b) Using K-map to simplify the equation obtained in (a).

* =By using Karnaugh Map (K-map) shown below, F CD AB 00 01 11 10 00 1 1 1 01 1 11 10 BCD+ĀCD BCD+ BCD ĀC+ ACD ĀC+ĀBD

Part 1 - Adders Let's consider a 8 bits precision system: a. Represent the number 81 in this system b. Represent the numbers 42 in this system c. Perform the following operation S = 81 +42 d. Represent the number (-42) within this binary system using the 2's complement representation e. Perform the following subtraction R = 42 - 81 in this system and prove that R = - 39 Let's consider that we have an IC that implements a four (4) bits adder. Use this IC to design an 8 bits adder g. Realize the addition S= 81 + 42 in this adder. You should write near each input and output operands of the ICs the value of each bit representing the Sum S f. h. Using the same design of question f, and any other additional circuitry, design a circuit that can realize a subtraction i. Simulate the subtraction presented in e. by showing the value of each input and output operands of the IC j. Simulate the addition presented in c. in this adder/subtractor by showing the value of each input and output operands…