Math Editor

Logic 2 Final Model 1

(1) Design a sequential circuit using the state diagram shown in figure 1, use D-flip flops.

DA = A'X'+AX = A XNOR X

Z = X'Y'+AXY

(2) Draw (ONLY) the following circuits:

• 4-bit up-down Synchronous counter.
• 4-bit register with load control.
• 3-bit shift left register.

(3) Define the following:

• Flip flop: A flip flop is a binary storage device capable of storing one bit of binary information.
• n-bit register: An n-bit register is a group of n flip-flops sharing a common clock source and is capable of storing n bits of binary information.
• n-bit counter. An n-bit counter is a register (a group of n flip flops) capable of counting from 0 to 2^n - 1.
• Serial and parallel loading (compare in a table).
  

(6) A building consists of 3 stages with an underground stage

it's needed to design the counter circuit for its lifter:

• Draw the required state diagram for the counter.
• Design the counter circuit using T flip flop.

flip flop B will flip in all cases except A'B'X' OR ABX

TB = (A'+B'+X') AND (A+B+X)

flip flop A will flip in two cases: A'BX + AB'X'

TA = A'BX + AB'X'

(7) A company produces 3 products A, B, and C as shown in the figure 2.

Find the money for selling product C (only) when the system stops.

components needed:

1. A register to store product C price (called C)
2. A register to store the sum (called D)
3. A full adder to update the sum

state flow:

1. load product c price in register c when start signal is sent
2. begin a loop
3. 1. check z: if z = 0 add c to sum
   2. continue

circuit realization

(8) Design an ALU to perform the following functions

for the arithmetic unit we will use a parallel adder

the stage will consist of a full adder with inputs Xi, Yi and Cin

and outputs Fi and C_i+1

for inputs could use a 4x1 mux to select Xi and the same for YI

or we could simplify Xi, Yi

lucky for us Xi is always Ai 😃

Bi = S0S1+S0S1'Bi'+S0'S1Bi = S1Bi + S0Bi'

for logic unit we will use a 4x1 multiplexer to select the output

then we will multiplex arithmetic and logic Fi based on S2

(9) Design an Accumulator to perform the following functions (Use J-K type):

for 1st function:

Ji=0

Ki=P1

for 2nd function:

Ji=P2

Ki=P2

for 3rd function:

Ji=P3A_i-1

Ki=P3(A_i-1)'

for 4th function:

Ji=P4Bi'

Ki=P4Ai

for 5th function:

Ci+1=AiBi+AiCI+BiCI

Ji=P5 AND (Bi'CI+BiCi')=P5(Bi XOR Ci)

Ki=P5(Bi XOR Ci)

Ji=P2+P3Ai-1+P4Bi'+P5(Bi XOR Ci)

Ki=P2+P3Ai-1'+P4Ai+P5(Bi XOR Ci)

(10) Using Table 1, find the Control Word for the following operations:

1. R2 = R1+1
2. R3 = R4+R5
3. R1 = shr R1
4. R2 = R7 – 1
5. R2 = crc R2
6. R6 = R7

1. 011 000 010 000 1 000
2. 100 101 011 001 0 000
3. 001 001 001 100 0 001
4. 111 000 010 011 0 000
5. 010 010 010 100 0
6. 111 000 110 000 0 000