Digital Electronics/Circuits Multiple Choice Questions on “Number System”.
1. The given hexadecimal number (1E.53)16 is equivalent to ____________
A. (35.684)8
B. (36.246)8
C. (34.340)8
D. (35.599)8
Answer: B
Clarification: First, the hexadecimal number is converted to it’s equivalent binary form, by writing the binary equivalent of each digit in form of 4 bits. Then, the binary equivalent bits are grouped in terms of 3 bits and then for each of the 3-bits, the respective digit is written. Thus, the octal equivalent is obtained.
(1E.53)16 = (0001 1110.0101 0011)2
= (00011110.01010011)2
= (011110.010100110)2
= (011 110.010 100 110)2
= (36.246)8.
2. The octal number (651.124)8 is equivalent to ______
A. (1A9.2A.16
B. (1B0.10)16
C. (1A8.A3)16
D. (1B0.B0)16
Answer: A
Clarification: First, the octal number is converted to it’s equivalent binary form, by writing the binary equivalent of each digit in form of 3 bits. Then, the binary equivalent bits are grouped in terms of 4 bits and then for each of the 4-bits, the respective digit is written. Thus, the hexadecimal equivalent is obtained.
(651.124)8 = (110 101 001.001 010 100)2
= (110101001.001010100)2
= (0001 1010 1001.0010 1010)2
= (1A9.2A.16.
3. The octal equivalent of the decimal number (417)10 is _____
A. (641)8
B. (619)8
C. (640)8
D. (598)8
Answer: A
Clarification: Octal equivalent of decimal number is obtained by dividing the number by 8 and collecting the remainders in reverse order.
8 | 417
8 | 52 — 1
8 | 6 – 4
So, (417)10 = (641)8.
4. Convert the hexadecimal number (1E2)16 to decimal.
A. 480
B. 483
C. 482
D. 484
Answer: C
Clarification: Hexadecimal to Decimal conversion is obtained by multiplying 16 to the power of base index along with the value at that index position.
(1E2)16 = 1 * 162 + 14 * 161 + 2 * 160 (Since, E = 14)
= 256 + 224 + 2 = (482)10.
5. (170)10 is equivalent to ____________
A. (FD.16
B. (DF)16
C. (AA.16
D. (AF)16
Answer: C
Clarification: Hexadecimal equivalent of decimal number is obtained by dividing the number by 16 and collecting the remainders in reverse order.
16 | 170
16 | 10 – 10
Hence, (170)10 = (AA.16.
6. Convert (214)8 into decimal.
A. (140)10
B. (141)10
C. (142)10
D. (130)10
Answer: A
Clarification: Octal to Decimal conversion is obtained by multiplying 8 to the power of base index along with the value at that index position.
(214)8 = 2 * 8v + 1 * 81 + 4 * 80
= 128 + 8 + 4 = (140)10.
7. Convert (0.345)10 into an octal number.
A. (0.16050)8
B. (0.26050)8
C. (0.19450)8
D. (0.24040)8
Answer: B
Clarification: Converting decimal fraction into octal number is achieved by multiplying the fraction part by 8 everytime and collecting the integer part of the result, unless the result is 1.
0.345*8 = 2.76 2
0.760*8 = 6.08 6
00.08*8 = 0.64 0
0.640*8 = 5.12 5
0.120*8 = 0.96 0
So, (0.345)10 = (0.26050)8.
8. Convert the binary number (01011.1011)2 into decimal.
A. (11.6875)10
B. (11.5874)10
C. (10.9876)10
D. (10.7893)10
Answer: A
Clarification: Binary to Decimal conversion is obtained by multiplying 2 to the power of base index along with the value at that index position.
(01011)2 = 0 * 24 + 1 * 23 + 0 * 22 + 1 * 21 + 1 * 20 = 11
(1011)2 = 1 * 2-1 + 0 * 2-2 + 1 * 2-3 + 1 * 2-4 = 0.6875
So, (01011.1011)2 = (11.6875)10.
9. Octal to binary conversion: (24)8 =?
A. (111101)2
B. (010100)2
C. (111100)2
D. (101010)2
Answer: B
Clarification: Each digit of the octal number is expressed in terms of group of 3 bits. Thus, the binary equivalent of the octal number is obtained.
(24)8 = (010100)2.
10. Convert binary to octal: (110110001010)2 =?
A. (5512)8
B. (6612)8
C. (4532)8
D. (6745)8
Answer: B
Clarification: The binary equivalent is segregated into groups of 3 bits, starting from left. And then for each group, the respective digit is written. Thus, the octal equivalent is obtained.
(110110001010)2 = (6612)8.