4.1/4.2- Decoders & Adders

Question 1

a way to create a circuit with multiple inputs based upon desired outputs.

Answer 1

minterm

Question 2

When do we use minterms

Answer 2

When we have the truth table but not a boolean expression and want to create a circuit

Question 3

What is the purpose of a multiplexer?

Answer 3

Pass through one of multiple inputs based upon a selection input.

Similar to an “if/else” statement in code.

Question 4

Kinda a reverse multiplexer
Select one of 2n data OUTPUTS to set high based on the binary value of the n control inputs
Possible enable switch

Uses:
Decode address lines in memory
Decode opcode (operation code) in CPU

Answer 4

Decoder

Question 5

Key component in an Arithmetic Logic Unit (ALU)
For ____ _____:
Thee Inputs: C{in}, x, y
Two Outputs: S & C

Answer 5

Full Adder

Question 6

given an example decoder with inputs s0 and s1 and outputs m0 - m3, the inside of the decoder will contain:

Answer 6

inputs s1 and not s1 as well as input s0 and not s0
the output gates will be 4 AND gates with two inputs each. from top to bottom inputs will be:
(s1 and s0)
(s1 and not s0)
(not s1 and s0)
(not s1 and not s0)

Question 7

given an example decoder with inputs s0, s1, and Enable (E) and outputs Q0 - Q3, the inside of the decoder will contain:

Answer 7

inputs s1 and not s1 as well as input s0 and not s0, and Enable (E)
the output gates will be 4 AND gates with three inputs each. from top to bottom inputs will be:
(s1 and s0 and E)
(s1 and not s0 and E)
(not s1 and s0 and E)
(not s1 and not s0 and E)

Question 8

a single bit full adder circuit has the inputs X, Y and Cin as well as the outputs C and S. What is the inner circuits formula?

Answer 8

C = yCin + xCin + xy
S = x ⊕ y ⊕ Cin

Question 9

a single bit full adder circuit has the inputs X, Y and Cin as well as the outputs C and S. What does the inner circuit look like?

Answer 9

Three AND gates with 2 inputs each, two xor gates and a or gate
(X AND Y)———
(X AND Cin)—— (OR) = C
(Y AND Cin)——-

(Y XOR Cin) XOR X = S

Question 10

What two things cause a carry in a look ahead adder?

Answer 10

x =1 && y=1 ← generation (g)
(x =1 || y=1) && Cin ← propagation (p)

Question 11

Carry look ahead adder formula

Answer 11

g= xy
p=x⊕y

Question 12

there is a carry to a higher bit if

Answer 12

Carry generated by current bit (g=1)

OR There is a carry from the lower bit AND the current bit can propagate it

Formula: C = g + pCin

Question 13

Look ahead adder input and output
g = _____
p = _____
S = _______

Answer 13

xy
x⊕y
x⊕y⊕Cin

Question 14

a full adder with inputs x, y, and c and outputs p, g, and s can be formed from the following circuit:

Answer 14

(X XOR Y) –|– p
(X AND Y) –|— g
C— XOR —— s