Question 1 (10 points): Express the following numbers in decimal A. (10110)2 B.

Question

Question 1 (10 points): Express the following numbers in decimal A. (10110)2 B. (26) C. (DADA)6 Question 2 (I0 points): Convert the following numbers to binary A. (2014)s B. (2014)6 Question 3 (10 points): Consider this binary number 100011011001 A. Convert this binary number to Octal B. How many bytes does this binary number have? C. What is the two's (2's) complement of this binary number? Question 4 (10 points): Perform the following 5-bit binary addition: 00111 + 01111 and state if there is an overflow Question 5 (10 points); A. What are the main functional units of the Von Neumann machine? B. Give a brief description of the function of each functional unit Question 6 (10 points): Write the truth table for Y = A+B.C

Explanation / Answer

Question 1 :

A.

(10110) base 2 = 1*(2^4) + 0*(2^3) + 1*(2^2) + 1*(2^1) + 0*(2^0) = 1*16 + 0*8 + 1*4 + 1*2 + 0*1 = 16+4+2 =

(22) base 10

B.

(26) base 8 = 2*(8^1) + 6*(8^0) = 2*8 + 6*1 = 16+6 = (22) base 10

C.

(DADA) base 16 = 13*(16^3) + 10*(16^2) + 13*(16^1) + 13*(16^0) = 13*4096 + 10*256 + 13*16 + 13*1 = 53248 + 2560 + 208 + 13 = (56029) base 10

Explanation:

The above conversions are done by multiplying the place values in the number with the respective powers of base to the place position number .

Place position number increases from right to left.

It starts from 0 as you can see in the above calculations.

Here the base is 2/8/16 .

Below is the table taken as reference to substitute the place values(decimal form) for each digit in the number.

Please refer the respective columns for each base.

Table:

Base 10|Base 2|Base 8|Base 16

0 0000 0 0

1 0001 1 1

2 0010 2 2

3 0011 3 3

4 0100 4 4

5 0101 5 5

6 0110 6 6

7 0111 7 7

8 1000 10 8

9 1001 11 9

10 1010 12 A

11 1011 13 B

12 1100 14 C

13 1101 15 D

14 1110 16 E

15 1111 17 F

16 10000 20 10

.

.

.

22 10110 26 16

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