Give a table of combinations for the boolean function

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Reference no: EM131005168

1. A half adder is a circuit that adds two bits to give a sum and a carry.Give the truth table for a half adder, and design the circuit using only two gates.Then design a circuit which will find the 2's complement of a 4-bit binary number. Use four half adders and any additional gates. (Hint: Recall that oneway to find the 2's complement of a binary number is to complement all bits, and then add 1.)

2. (a) Write the switching functionj (x,y) = x + y as a sum of minterms and as a product of maxterms.

(b) Consider the Boolean algebra of four elements {o, 1, a, b} specified lby the following operation tables and the Boolean functionj(x,y) = ax + by where a and b are two of the elements in the Boolean algebra .Writej(x,y) in a sum-of-minterms form.

(c) Write the Boolean function of part (b) in a product-of-maxterms form.

(d) Give a table of combinations for the Boolean function of Part (b).(Note:The table of combinations has 16 rows, notjus t 4.)

(e) Which four rows of the table of combinations completely specify the function of Part (b)? Verify your answer.

 

+

0

1

a

b

 

0

1

a

b

0

1

 

0

0

1

a

b

 

0

0

0

0

0

1

0

 

 

 

1

1

 

 

 

0

1

a

b

a

b

 

a

a

1

a

 

 

a

0

a

a

0

b

a

 

b

b

1

1

b

 

b

0

b

0

b

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Reference no: EM131005168

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