ELEC2200 Digital Logic Circuits Spring 2021 Prelim1 (4 Questions)

• You must not communicate with or get help from anyone during this exam.
• You must use the same layout of K-map as used in class.

1. You must use the power-series expansion (only for non-decimal to decimal), successive division,
and/or successive multiplication in any number conversion.

(a) Represent the octal number (137.6)8 in the base-3 number system, using up to 8 digits.

(b) Represent the decimal number (−111)10 in the 8-bit signed 2’s complement binary number
system, and then express it in 10 bits (signed 2’s complement).

2. A and B below are two numbers represented in the 8-bit signed 2’s complement binary number
system. Perform the indicated arithmetic operation using the 2’s complement arithmetic and
determine (with an explanation) if an overflow occurs or not. Also, express the result in the
sign+magnitude format (use 9 bits in the case of overflow).
(a) A=10100000, B=00110000, A – B
(b) A=01010000, B=11100000, – A + B

3. Derive the minimal SOP (sum of products) expression of the function F(W,X,Y,Z) given below.
(, , , ) = ∑ (1,11,13,14) + (0,5,8,9,10,12)

4. F(W,X,Y,Z) is a binary function of which the input (4-bit binary number, WXYZ) is always less than 12
(decimal). When the number of 1’s in the input (W,X,Y,Z) is 2 or 3, F(W,X,Y,Z) is 1. Otherwise,
F(W,X,Y,Z) is 0. The complexity of digital circuit realizing the function is to be reduced as much as
possible. Derive the truth table of F(W,X,Y,Z) and find the minimal POS (product of sums) expression.
Also, draw a digital circuit realizing the minimal POS with random logic gates of any type and size.

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