By designing circuits that can process sums and carries efficiently, computers can speed up arithmetic operations, which is critical in processors and digital systems.
Q: The decimal equivalent of binary number 0.0111 is -
4.375
0.4375
0.5375
-0.4375
[ Option B ]
Binary Digit | Position | Power of 2 | Decimal Contribution |
---|---|---|---|
0 | 1 | 2-1 | 0 × 1/2 = 0 |
1 | 2 | 2-2 | 1 × 1/4 = 0.25 |
1 | 3 | 2-3 | 1 × 1/8 = 0.125 |
1 | 4 | 2-4 | 1 × 1/16 = 0.0625 |
Finally sum the number 0 + 0.25 + 0.125 + 0.0625 = 0.4375
Q: Which of the following values is the correct value of this hexadecimal code 1F.01B?
35.0065918
32.0065918
31.0065918
30.0065918
[ Option C ]
To convert the hexadecimal number (1F.01B)16 into its decimal equivalent, we first separate it into the integer part (1F) and the fractional part (.01B).
In integer part conversion, each digit is multiplied by 16 raised to the power of its position from right to left, starting with 0.
(1F)16 = 1⋅161+F⋅160 = 16+15 = 31
In fractional part conversion, each digit after the hexadecimal point is multiplied by 16 raised to a negative power corresponding to its position.
0⋅16−1+1⋅16−2+B⋅16−3 = 0 + 0.00390625 + 0.002685546875 = 006591796875 ≈ 0.0065918
After combining integer and fractional parts, 31 + 0.0065918 = 31.0065918
Q: Find x = ? If (356)8 = (x)16
EE
EA
7E
A8
[ Option A ]
To quickly convert a number from octal to hexadecimal, first convert the octal number into binary by replacing each octal digit with its 3-bit binary equivalent. Then, group the binary digits into 4-bit groups starting from the right. Finally, convert each 4-bit group into its hexadecimal equivalent.
For example, to convert 3568to hexadecimal:
So, 3568 = EE16.
Q: The decimal number represented by the binary number (0.10101) is :
(0.56)10
(0.6875)10
(0.3125)10
(0.65625)10
[ Option D ]
The binary fraction (0.10101)2 is converted to decimal by multiplying each digit with 2−n, where n is the position after the decimal point. Thus, it becomes 1×2−1 + 0×2−2 + 1×2−3 + 0×2−4 + 1×2−5. This equals 0.5 + 0 + 0.125 + 0 + 0.03125 = 0.65625. Therefore, the decimal equivalent of (0.10101)2 is (0.65625)10.
Q: Binary Coded Decimal (BCD) numbers express each digit in a –
Bit
Byte
Nibble
All of the above
[ Option C ]
Binary Coded Decimal (BCD) is a method of representing each decimal digit (0 to 9) using a fixed number of binary bits. Each decimal digit is encoded using 4 bits, which is exactly half a byte and commonly called a nibble.
Decimal Digit | BCD Representation |
---|---|
0 | 0000 |
1 | 0001 |
2 | 0010 |
3 | 0011 |
4 | 0100 |
5 | 0101 |
6 | 0110 |
7 | 0111 |
8 | 1000 |
9 | 1001 |
Q: Hexadecimal numbers are a mixture of -
Octal and decimal numbers
Binary and octal numbers
Letters and decimal digits
Binary and decimal numbers
[ Option C ]
The hexadecimal number system is a base-16 positional numeral system used widely in computing and digital electronics. It uses 16 distinct symbols to represent values from 0 to 15:
Number System | Base | Symbols Used | Example |
---|---|---|---|
Binary (Internally used by Computers) | 2 | 0 and 1 | 101001 |
Octal (Rarely used Today) | 8 | 0 to 7 | 1702 |
Decimal (Standard Number System used by Humans) | 10 | 0 to 9 | 47921 |
Hexadecimal (Widely used in Computing for Memory Addresses and Color Codes) | 16 | 0 to 9, A to F Where A = 10 and F = 15 | 8F0AE |
Q: Which of the following is a valid BCD representation of the decimal number 79?
100 1111
1111 0000
1000 1001
0111 1001
[ Option D ]
Q: One’s complement representation of (-8)10 is :
(01000)2
(10111)2
(11000)2
(00111)2
[ Option B ]
In one’s complement representation, a negative number is obtained by inverting all the bits of its positive binary form. For (−8)10, we first write +8 in 5-bit binary, which is (01000)2. Now, by inverting each bit (all 0s become 1s and all 1s become 0s), we get (10111)2. Hence, the one’s complement representation of (−8)10 is (10111)2.
Q: Which of the following binary numbers represents an invalid BCD code?
0101
1001
0111
1011
[ Option D ]
BCD (Binary-Coded Decimal) represents decimal digits 0 to 9 using 4-bit binary codes.
Decimal | BCD Code |
---|---|
0 | 0000 |
1 | 0001 |
2 | 0010 |
3 | 0011 |
4 | 0100 |
5 | 0101 |
6 | 0110 |
7 | 0111 |
8 | 1000 |
9 | 1001 |
🔶 BCD Valid Range: 0000 to 1001
🔶 1011 = 11 (which is not a valid decimal digit in BCD)
Q: Which of the following is equivalent to decimal 255 in hexadecimal?
EE
FF
F0
FE
[ Option B ]
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