Question

3. Convert the following signed hexadecimal numbers to decimal .

a) EE2

b) 7F2

c) 2FE

4. Perform the subtractions with the following binary numbers using 2’s complement

Check the answer by straight binary subtractions. a) 10011 – 10001,

b) 10110 – 11000,

c) 100111011 – 10001.

5. What is the decimal equivalent of the largest binary integer that can be obtained with

a) 11 bits unsigned signed

b) 25 bits? unsigned signed

Answer 1

According to HomeworkLib policy we answer first Four Sub parts., but I answer 6 for u.

3) For Hexadecimal to Decimal

Hexadecimal	1	2	3	4	5	6	7	8	9	A	B	C	D	E	F
Decimal	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15

a) (EE2)₁₆

= (14 × 16²) + (14 × 16¹) + (2 × 16⁰)

= (14 × 256) + (14 × 16) + (2 × 1)

= (3584) + (224) + (2)

= (3810)₁₀

b) (7F2)₁₆

= (7 × 16²) + (15 × 16¹) + (2 × 16⁰)

= (7 × 256) + (15 × 16) + (2 × 1)

= (1792) + (240) + (2)

= (2034)₁₀

c) (2FE)₁₆

= (2 × 16²) + (15 × 16¹) + (14 × 16⁰)

= (2 × 256) + (15 × 16) + (14 × 1)

= (512) + (240) + (14)

= (766)₁₀

4) For Binary Subtraction

0-0 = 0

1-0 = 1

1-1 = 0

a) 10011 – 10001

(10011)₂ = (1 × 2⁴) + (0 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰) = (19)₁₀

( 10001)₂ = (-16 × 2⁵) + (1 × 2⁴) + (0 × 2³) + (0 × 2²) + (0 × 2¹) + (1 × 2⁰) = (17)₁₀

10011

- 10001

______________

2 = 00010

_______________

b) 10110 – 11000

(10110)₂ = (1 × 2⁴) + (0 × 2³) + (1 × 2²) + (1 × 2¹) + (0 × 2⁰) = (22)₁₀

(11000)₂ = (1 × 2⁴) + (1 × 2³) + (0 × 2²) + (0 × 2¹) + (0 × 2⁰) = (24)₁₀

10110

- 11000

______________

-2 = 11110

____________________

c) 100111011 – 10001.

(100111011)₂ = (1 × 2⁸) + (0 × 2⁷) + (0 × 2⁶) + (1 × 2⁵) + (1 × 2⁴) + (1 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰) = (315)₁₀

(10001)₂ = (1 × 2⁴) + (0 × 2³) + (0 × 2²) + (0 × 2¹) + (1 × 2⁰) = (17)₁₀

100111011

- 000010001

______________

298 = 0100101010