computer organozation and archtiteture

1. Convert the followings:

a. 0xAC12 to binary

b. -107₁₀ to 8-bit 2’s Complement
c. 10011110 (8-bit 2’s complement representation) to decimal

d. 1101011010₂ into hexadecimal

e. 110₈ into hexadecimal

2)The following binary number is stored using the floating point representation of IEEE-754 single precision format. Find out the value in decimal.

11101000011010000000000000000000

3)Using basic Boolean algebra identities, prove that ABC+ABC'+AB'C+A'BC = AB + AC + BC. Please show all steps and mention the identities used.

4)1. Design a digital combinational circuit which compares two 2-bit binary numbers and produces results using a 2-bit binary number (please see the block diagram below). The outputZ₁Z₀depends on the inputsA₁A₀andB₁B₀according to the following criteria:

• If (A₁A₀ > B₁B₀) the output Z₁Z₀ = 10
• If (A₁A₀ B₁B₀) the output Z₁Z₀ = 01
• If (A₁A₀ = B₁B₀) the output Z₁Z₀ = 11

You should use minimum number of logic gates.

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