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313303 - Digital Techniques (Sem III)
As per MSBTE’s K Scheme
CO / CM / IF
Unit I Number Systems Marks - 08
Sr. Questions Year Marks
No.
1 Write the radix of binary, octal, decimal and hexadecimal number system. W-18 2
State the base of following number system Decimal, binary, Octal,hexadecimal S-23 2
Ans Radix of: Binary – 2
Octal - 8
Decimal - 10
Hexadecimal -16
2 Convert - W-18 4
(i) (255)10 = (? )16 = (? )8
(ii) (157)10 = (? )BCD = (? ) Excess3
1
3 Subtract using 2’s compliment method W-18 6
(35)10 – (5)10
Ans Step 1 – Obtain binary equivalent of (35)10& (5)10 & then take 2’s complimentof (5)10.
i.e. (35)10 = (100011)2
(5)10 = (101)2
2’s compliment of (5)10 = (000101)2 = 111010 1’s compliment
+ 1
(111011)2 2’s Compliment
Step -2 : Now add (100011)2 and (111011)2
100011
+ 111011
1 011110
2
Carry is generated so answer is in positive form, so will
discard the carry generated
Therefore final answer will be (011110)2 = (30)2
4 Convert (D8F)16 into binary and octal W-19 2
Ans
5 Perform the subtraction using 2'S Complement methods. W-19 4
(52)10 – (65)10
Ans
3
6 (i) Convert the following binary number (11001101)2 into Gray Code and Excess-3 Code. W-19 6
(ii) Perform the BCD Addition.
(17)10 + (57)10
(iii) Perform the binary addition.
(10110 • 110)2 + (1001 • 10)2
Ans
4
7 List the binary, octal and hexadecimal numbers for decimal no. 0 to 15 S- 19 2
Ans
8 Write the gray code to given no. (1101)2 = (?) Gray. S-19 2
Ans
5
9 Convert: S-19 4
Ans (i) (AD92.BC A) 16 = (?)10 = (?)8 = (?)2
(AD92.BCA)16
= (10 × 16³) + (13 × 16²) + (9 × 16¹) + (2 × 16⁰) + (11 × 16⁻¹) + (12 × 16⁻²) + (10 × 16⁻³)
= 40960 + 3328 + 144 + 2 + 0.6857 + 0.046875 + 0.00244
= (44434.7368)10
(AD92.BCA)16 =(1010 1101 1001 0010.1011 1100 1010)2
(AD92.BCA)16 = (1010 1101 1001 0010.1011 1100 1010)2
=(001 010 110 110 010 010.101 111 001 010)2
=(126622.5712)8
Note: any other method can be considered.
10 Subtract the given number using 2’s complement method: S-19 4
Ans (i) (11011)2 – (11100)2
(ii) (1010)2 – (101)2
i) Subtract (11011)2 – (11100)2using 2’s complement binary arithmetic.
Solution:
(11011)2 – (11100)2
Now,
2’s complement of (11100)2= 1’s complement of (11100)2+1 1’s complement of (11100)2 =
(00011)2
2’s complement = 00011+1 = 00100
6
Therefore, 1 1 0 1 1
+
0 0 1 0 0
1 1 1 1 1
There is no carry it indicates that results is negative and in 2’s complement form
i.e.(11111)2. Therefore, for getting true value i.e.(+1) take 2’s complement of (11111) is
1’s complement + 1
= 00000 + 1
Ans= (00001)2
Ans: (11011)2 – (11100)2 = 2’s complement of (11111)2 = (-1)10
ii) Subtract (1010)2 - (101)2using 2’s complement binary arithmetic.
2’s complement of (0101)2 = 1’s complement of (0101)2 +1
1’s complement of (0101)2 = (1010)2
2’s complement = 1010+1 = 1011
Therefore, 1 0 1 0
+
1 0 1 1
1 0 1 0 1
There is carry ignore it, which indicates that results is positive i.e.(+5)
= (0101)2
Ans: (1010)2 - (101)2 = (0101)2= (+5)10
11 Write gray code to given number (11111)2 = (?)Gray W-22 2
Ans
7
12 Convert the following. W-22 6
i) (6AC) 16 = (?)10
ii) (2003)10 = (?)16
iii) (228)10 = (?)BCD
Ans
8
13 Convert (1101011)2 = ( ) 16 and (1111011)2 = ( ) 8 S-22 2
Ans
9
14 Convert (43)10 = (BCD) S-22 4
(34)10 = (Excess-3)
(110111)2 = (Gray)
(11101)2 = (2’s complement)
10
11
15 Subtract following using Two’s complement method. S-22 6
(15)10 – (32)10
12
16 List the octal and hexadecimal numbers for decimal number 0 to 15. W-23 2
13
17 Convert (159)10 = ( ? )8 W-23 2
Convert (380)10 = ( ? )16
14
15
18 Perform the subtraction using 2’s complement methods. W-23 4
(10110)2 – (11010)2
16
19 Convert (53)10 = (BCD) W-23 4
(34)10 = (Excess-3)
(100111)2 = (Gray)
(11010)2 = (2’s complement)
17
20 Convert the given binary into decimal, octal, hexadecimal and gray code: S-23 4
(10110101)2
18
19
20
21 i) State the rules of BCD addition. S-23 6
ii) Perform BCD addition of : (972)10 + (348)10
21
22 Perform the following subtraction using 2’S compliment method. S-24 4
I) (1100)- (0011)
II) ( 10101)- (11100)
22
23 Convert the following S-24 4
I) (ABCD) 16 = (?)10
II) (101011001111)2 = (?)10
III) (101011001111)2= (?)8
i) (ABCD)16 = ( ? ) 10
ii) (101011001111)2 = (?)10
23
(101011001111)2 = (?)8
24 List the uses of following codes. S-24 2
I) BCD code
II) ASCII
The uses of following codes are:
i) BCD Code:
1) In digital communication
2) In Digital computers
3) In many personal computers to store date and time
4) In other digital systems where, precise decimal arithmetic operationsare
required e.g. calculators.
5) In real time clock systems
ii) ASCII:
24
1) In computers to represent characters, symbols and alphabets.
2) Most computer keyboards are standardized using ASCII.
3) ASCII is standard for character encoding used in appliances,
telecommunications, computers and other related devices.
It is used to display text in various devices.
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