QUESTION 1
[40]
1.1 Convert Binary 111011.11 to Hexadecimal
1.2 Convert 673_(8) to Decimal.
1.3 Using Boolean algebra techniques, simplify the following expression.
x()/(b)=ar (A)/(b)ar (B)/(b)ar (C)(+)/(b)ar (A)/(b)ar (B)C(+)/(b)ar (A)/(b)ar (C)
1.4 Determine the 2's complement of 10000011_(2)
1.5 Perform the following additions:
(a) 564_(8)+726_(8)
(b) 1111_(2)+1111_(2)
(c) 9B_(16)+6E_(16)
1.6 Write the expression in sigma notation:
x_((ABCD))=A(B)/(b)ar (C)/(b)ar (D)+(A)/(b)ar (B)CD(+)/(b)ar (A)(B)/(b)ar (C)/(b)ar (D)(+)/(b)ar (A)/(b)ar (B)(C)/(b)ar (D)+(A)/(b)ar (B)/(b)ar (C)/(b)ar (D)
1.7 What is the output of a XNOR gate when two inputs are HIGH?
1.8 Which logical gate is called as an universal gate with which any Boolean function can be implemented?
QUESTION 2
30
2.1 Simplify the expression
/bar (W)(x)/(b)ar (Y)Z+W(x)/(b)ar (Y)Z+W(x)/(b)ar (Y)/(b)ar (Z)+W(ar{x} )/(b)ar (Y)/(b)ar (Z)(+)/(b)ar (W)ar{x} YZ(+)/(b)ar (W)xYZ+War{x} YZ+War{x} (Y)/(b)ar (Z)
using a Karnaugh map.
Please note: use WX in the rows and YZ in the columns
2.2 Write the expanded forms of the terms in the given expression:
F(ABCD)=(A)/(b)ar (B)C+ACD+AB(C)/(b)ar (D)
[TURN OVER]
QUESTION1
[40]
1.1Convert Binary 111011.11 to Hexadecimal
(5)
1.2Convert 673to Decimal
(5)
1.3Using Boolean algebra techniques,simplify the following expression
(6)
X=ABC+ABC+AC
1.4Determine the 2's complement of 100000112
(3)
1.5Perform the following additions:
a564+7268
(4)
(b) 11112+11112
(4)
(c) 9B+6E6
(4)
1.6 Write the expression in sigma notation:
XABCD=ABCD+ABCD+ABCD+ABCD+ABCD
(5)
1.7 What is the output of a XNOR gate when two inputs are HIGH?
(2)
1.8 Which logical gate is called as an universal gate with which any Boolean function can be implemented? (2)
QUESTION2
[30]
2.1Simplify the expression
WXYZ+WXYZ+WXYZ+WXYZ+WXYZ+WXYZ+WXYZ+WXYZ
using a Karnaugh map.
(9)
Please note:use WX in the rows and YZ in the columns
2.2 Write the expanded forms of the terms in the given expression:
(5)
F(ABCD=ABC+ACD+ABCD
[TURN OVER]