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Instructions:
1. Times New Roman 12 pt font should be used for all writing. Answer all questions
in English.
2. The deadline for the submission of TMA 1 is during Tutorial 2.

Question 1

(a) Briefly explain the following representation: sign magnitude, two complement and
biased. Describe how to determine if a number is negative for the above representations.

(b) Find the following differences using two’s complement arithmentic:
(i) 111101 (ii) 10101110 (iii) 111110010111 (iv) 11101001
-100110 – 111010 – 111010010101 – 10011010

Question 2

(a) Represent the following decimal numbers in both binary sign/magnitude and two’s
complement using 16 bits: +402 and -14

(b) Assume numbers are represented in 8-bit 2’s complement representation. Show the
calculation of the following:
(i)6 + 13 (ii) -6 + 13 (iii) 6 – 13 (iv) -6 -13

(c) Find the equivalent decimal value for the following numbers in IEEE 32-bits floatingpoint format
(i) 1 10000110 11000000000000000000000

(ii) 0 01111110 10110010000000000000000

(iii)0 10000001 00000000000000000000000

Question 3

a. Develop a truth table for this circuit.
b. Express the truth table in SOP form.
c. Express the truth table in POS form.
d. Provide a simplified expression.

10110010000000000000000

(iii)0 10000001 00000000000000000000000

Question 3

a. Develop a truth table for this circuit.
b. Express the truth table in SOP form.
c. Express the truth table in POS form.
d. Provide a simplified expression.

. Describe how to determine if a number is negative for the above representations.

(b) Find the following differences using two’s complement arithmentic:
(i) 111101 (ii) 10101110 (iii) 111110010111 (iv) 11101001
-100110 – 111010 – 111010010101 – 10011010

Question 2

(a) Represent the following decimal numbers in both…