Place the computing technologies in the proper chronological order.

Question

(1-1) Place the computing technologies in the proper chronological order corresponding to when they were first introduced, from earliest to most recent:

integrated circuits

mechanical – machine powered

mechanical – manually powered

transistors:

vacuum tubes

 

(2-1) The binary representation of the hexadecimal number 3B7F is (choose one):

(A) 0100 1001 1110 1101

(B) 0011 1011 0111 1111

(E) 1101 1100 1011 0101

(C) 0010 0100 0000 1010

(D) 0110 0011 1011 1100

 

(2-2) Convert the following numbers as indicated.

(a) (110101)₂ to unsigned base 10.

(b) (-29) to two’s complement (use 8 bits in the result).

(c) (61543), to unsigned base 16 (use four base 16 digits in the result).

(d) (37)₁0 to unsigned base 3 (use four base 3 digits in the result).

 

(2-3)  A computer with a 32-bit word size uses two’s complement to represent numbers. The range of integers that can be represented by this computer is:

(A) 232 to 232

(B) 2³1 to 232

(C) 231 to 231-1

(D) 232 to 23

(E) 232-1 to 232

 

Explanation

1-1) Initially, computing relied on mechanical-manual power technology. The first machine computer was introduced in 1837 by Charles Babbage, thanks to advances in science and technology. Vacuum tubes were first used in computer technology in 1951. Then came transistors, followed by integrated circuits, which made computer systems smaller and more portable in computing.
As a result, they are organized as follows: mechanically powered, mechanically powered by machine, vacuum tubes, transistors, and integrated circuits.

 

2-1) 3B7F in binary is:

3 is 0011

B is 1011

7 is 0111

F is 1111

So, the complete representation is 0011 1011 0111 1111.

The correct answer is (B).

2-2) 110101 in unsigned base 10

= 1.2⁵ + 1.2⁴ +0. 2³ + 1.2² + 0.2¹+ 1.2⁰

= 32+ 16+ 4+1

= 53

 

 

b) 29

To get the binary of negative number, we can use two’s complement of the number

Binary of 29 is: 0001 1101

1’s complement: 1110 0010

2’s complement: 1110 0011

 

 

c) 61543 is an octal number. To convert it to a hexadecimal number, we convert it into a binary number and then to hexadecimal. To convert it into binary, we simply write the binary code of each number in 3-bit (less than 8).

6             1                  5                  4                  3

110         001              101              100              011

The binary number is 110 001 101 100 011

To convert it to hexadecimal, we make a group of 4 bits (16 is represented in 5 bit) and write the hexadecimal value of that number.

0110 0011 0110 0011

6             3        6        3

The hexadecimal value is 6363.

 

d) 37 is in decimal. To convert it to base 3, we divide the number by 3 continuously and store the remainder.

3        37      1

3        12      0

3        4        1

3        1        1

0

Ans- 1101

 

 

2-3) c) -2³¹ to 2³¹-1

Range of two’s complement od n bits is given by,

-2^n-1 to +2^n-1-1.

So, we replace n with 32 and get the range.

 

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