# computer organozation and archtiteture

1. Convert the followings:

a. 0xAC12 to binary

b. -107 10 to 8-bit 2’s Complement
c. 10011110 (8-bit 2’s complement representation) to decimal

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 output Z 1Z 0depends on the inputs A 1 A 0and B 1 B 0according to the following criteria:

• If ( A 1 A 0 >  B 1 B 0) the output  Z 1 Z 0 = 10
• If ( A 1 A 0  B 1 B 0) the output  Z 1 Z 0 = 01
• If ( A 1 A 0 =  B 1 B 0) the output  Z 1 Z 0 = 11

You should use minimum number of logic gates.

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