Question 1:

(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:

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.