J277 1.2 Practice

What is the binary equivalent of the denary number 5?

(a)  

Answer explanation

The binary equivalent of the denary number 5 is 00000101. This is derived by converting 5 into binary, where 1 represents the value and 0 represents the absence of value in each bit position.

Convert the binary number 11010111 to denary.

(a)  

Answer explanation

To convert the binary number 11010111 to denary, calculate: 1*2^7 + 1*2^6 + 0*2^5 + 1*2^4 + 0*2^3 + 1*2^2 + 1*2^1 + 1*2^0 = 128 + 64 + 0 + 16 + 0 + 4 + 2 + 1 = 215. Therefore, the correct answer is 215.

What is the denary equivalent of the binary number 10101010?

(a)  

Answer explanation

To convert the binary number 10101010 to denary, calculate: 1*2^7 + 0*2^6 + 1*2^5 + 0*2^4 + 1*2^3 + 0*2^2 + 1*2^1 + 0*2^0 = 128 + 0 + 32 + 0 + 8 + 0 + 2 + 0 = 170. Therefore, the denary equivalent is 170.

Convert the denary number 18 to an 8-bit binary number.

(a)  

Answer explanation

To convert the denary number 18 to binary, divide by 2 repeatedly: 18/2=9, 9/2=4, 4/2=2, 2/2=1, 1/2=0. The remainders read from bottom to top give 10010. As an 8-bit binary, it's 00010010, which is the correct answer.

What is the binary equivalent of the denary number 255?

(a)  

Answer explanation

The binary equivalent of the denary number 255 is 11111111. Each bit represents a power of 2, and 255 in binary is achieved by setting all 8 bits to 1.

Add the binary numbers 11001001 and 00011110.

(a)  

Answer explanation

To add the binary numbers 11001001 and 00011110, align them and add each column from right to left, carrying over when the sum exceeds 1. The correct sum is 11100111, but the answer choices indicate 0, which is incorrect.

Add the binary numbers 10101010 and 01010101.

(a)  

Answer explanation

To add the binary numbers 10101010 and 01010101, align them and add each column, carrying over as needed. The result is 11111111, which is 255 in decimal. However, the correct answer is 0, indicating a misunderstanding in the question.

What happens if the sum of two binary numbers exceeds 8 bits?

(a)  

Answer explanation

When the sum of two binary numbers exceeds 8 bits, the result wraps around, discarding the overflow bits. Therefore, the correct answer is 0, as it represents the value after the overflow.

Add the binary numbers 11111111 and 00000001. What happens?

(a)  

Answer explanation

Adding 11111111 (255 in decimal) and 00000001 (1 in decimal) results in 100000000 (256 in decimal). In an 8-bit system, this exceeds the maximum value (255), causing an overflow. Thus, the result is 0 due to wrap-around.

Convert the denary number 30 to hexadecimal.

(a)  

Answer explanation

To convert the denary number 30 to hexadecimal, divide 30 by 16. The quotient is 1 and the remainder is 14. In hexadecimal, 14 is represented as 'E'. Therefore, 30 in hexadecimal is 1E, but the correct answer is 0, indicating a mistake in the choices.