Question

The following 5 questions use two's complement representation.  
You MUST use 5 (five) bit binary.  (ex. 000012)  
DO NOT Extend beyond 5 bits.
A = +13          B = +4             C = -6

a.) A - B = _______________ ₂       

b.) A - B results in overflow. true or false?

c.)C + A = _{_____________ 2}

_d.)C + A results in overflow. true or false?

e.) C - A = ______________________₂

_f.) C - A results in overflow. true or false?

g.)B + A = ______________________₂

_h.) B + A results in overflow. true or false?

i.) B - A = _______________________₂

_j.) B - A results in Overflow. true or false?

Answer 1

Given that the number system is five bit binary 2's complement.

A = +13 = (01101)₂

B = +4 =  (00100)₂

C = -6 =  (11010)₂

a) A- B = (01001)₂ = +9

b) There is no overflow, Since Cin = Cout

c) C+A = (00111)₂ = +7

d) There is no overflow, Since Cin = Cout

e) C-A = (101101)₂ = -19

f) There is overflow, Since Cin ≠ Cout.

g) B+A = (010001)₂ = +17

h) There is overflow, Since Cin ≠ Cout

i) B - A = (10111)₂ = -9

j) There is no overflow, Since Cin = Cout

Note:

Cin is nothing carry generated by (MSB-1) th bits of both operands.

Cout is nothing carry generated by (MSB) th bits of both operands.