# Worksheet 4 Chapter 1 to Chapter 4 Question 1: Calculate the following:

```Worksheet 4
Chapter 1 to Chapter 4
Question 1:
Calculate the following:
a) (11101)2 * (110)2
b) (1110)2 + (1100)2
c) (10110)2 – (01010)2
Question 2:
Subtract the following:
a) (56)8 – (AC) 16, using 10’s complement.
b) (1110)2- (25)10, using (r’s) complement.
Question 3:
Study the following two functions and answer the following:
F (A, B, C) = AꞌBꞌ + B (A+C)
F (A, B, C) = BC + ACꞌ
b) If the functions were equal, draw the logic circuit for the function
that you think is better to use and justify why you choose that
function. If they were not equal, draw the logic circuit for both
functions.
Question 4:
Simplify (minimize) the following functions to a minimum number of literals.
a) F1=xyz + xꞌy + xyzꞌ
b) F2= (A+B)ꞌ(Aꞌ+Bꞌ)
Question 5:
Express the following Boolean functions in
 Standard Sum of Minterms.
 Canonical product of sums form.
a) F1 (A, B, C) =A+BꞌC
b) F2(x, y, z) = x y + xꞌ z
c) F3 (x, y, z) = x(y + z)
Question 6:
Convert the following to the other canonical form:
a) F (x, y, z)= ∑(1,3,7).
b) F (A, B, C, D) = П(0,2,4,6,8,10,12,14).
c) F ꞌ(x, y, z)= ∑(2,4,5,6).
Miss. Dareen Hamoudeh
Question 7:
Form the following truth table
a) Extract the function (f1) in SOP, and write its
minterms notation.
b) Extract the function (f2) in POS, and write its
maxterms notation.
c) Extract the function (fꞌ1) in SOP, and write its
minterms notation.
Question 8:
Find the complement for the following Boolean expressions:
a) F1 =x yꞌ + xꞌ y
b) Y = (AB+C) Dꞌ+E
c) F2 = (x + yꞌ+z)(xꞌ+y)(xꞌ+zꞌ)
Question 9:
Simplify the following Boolean function using K-map.
F(w, x, y, z)=∑(0,2,3,5,7,8,9,10,11,13,15)
Question 10:
Given the function F (w, x, y, z) =xꞌ z + wꞌ x yꞌ + w (xꞌ y + x yꞌ), Use K-map to the
following:
a) The simplified function in sum of products form.
b) The simplified function in product of maxterms.
c) The simplified complement (Fꞌ) in SOP form.
Question 11:
Solve the question in chapter 4 (Simplification Using Map Method) slide number 73
Question 12:
Given the following K-map, extract the canonical function in SOP.
Miss. Dareen Hamoudeh
```