ITI1100 Digital Systems I Midterm examination complete solutions correct answers key

ITI1100 Digital Systems I Midterm examination complete solutions correct answers key

Winter 2013

Question 1 (40 points: 15 + 10+ 15):
(a) Convert the following binary into (i) decimal, (ii) octal et (iii) hexadecimal 10100001111.1101

(b) Perform the following operation using 10’s complement

(162)10 – (27)10

(c) Convert the following numbers into binary and perform the arithmetic operations in (i)
and (ii) using signed binary numbers with 2’s complement. Use 7 bits to represent the
integer part of decimal numbers and the sign bit. Use three bits to represent the fractional
part.
(i) (4.5)10 – (9)10
(ii) (8.5)10 + (9)10

Question 2: (10 + 30 + 5 + 15 = 60 points)
Design a 4- bit combinational circuit 2’s complementer. The circuit generates at the output
the 2’s complement of the input binary numbers.
Answer the following questions:
(i) Complete the following truth table. A,B,C,D indicate the input binary number to be
complemented using 2’s complement and W,X,Y, Z represent the output 2’s complement of
the input binary number. The variable D is the least significant bit and A is the most
significant bit of the binary number.

(ii) Simplify the Boolean function W in its Sum of Products form using K-Map

(iii) Show that the Boolean function W can be constructed using exclusive-OR gates

(iv) Implement the Boolean function Z in its Product of Sums form with a decoder
constructed with NAND gates (see figure below) and external gate (s) connected to the
decoder outputs.