Number System Questions and Answers

Answer: B

Correct answer: Multiplying

The integer part of a decimal number is converted by repeated division by 2, taking the remainders. A fraction is converted the other way: multiply repeatedly by 2 and take the integer part that carries out each time. For example \(0.625\times 2 = 1.25\) gives 1, \(0.25\times 2=0.5\) gives 0, \(0.5\times 2=1.0\) gives 1, so \(0.625_{10}=0.101_2\).

Answer: A

Correct answer: (140)10

\[ 214_8 = 2\times 64 + 1\times 8 + 4 = 128+8+4 = 140 \]

Answer: B

Correct answer: 100

\(1+1+1+1 = 4\), and four in binary is 100. The other options are not equal to four: 111 is 7, 1111 is 15 and 1001 is 9.

Answer: A

Correct answer: 491

Each octal digit carries a power of 8:

\[ 753_8 = 7\times 64 + 5\times 8 + 3 = 448+40+3 = 491 \]

Answer: C

Correct answer: (AA)16

Divide by 16 and read the remainders upward:

\[ 170 \div 16 = 10 \ \text{remainder}\ 10 \]

Both the quotient and the remainder are 10, which is A in hexadecimal, so the answer is AA. As a check, \( A\!A_{16} = 10\times 16 + 10 = 170 \).

Answer: C

Correct answer: 421

Each octal digit carries a power of 8:

\[ 645_8 = 6\times 8^2 + 4\times 8^1 + 5\times 8^0 = 384+32+5 = 421 \]

Answer: B

Correct answer: nibble

A nibble is four bits, and four bits are exactly what one hexadecimal digit represents - which is why two hex digits make a byte. That correspondence is the reason hexadecimal is used for binary data at all.

Answer: D

Correct answer: 11

In binary, \(1+1+1 = 3\), and three is written 11 - one two plus one one. In an adder this appears as a sum bit of 1 with a carry of 1.

Answer: A

Correct answer: binary

Digital circuits have two stable states, high and low, so they represent numbers in base 2. Octal and hexadecimal are used by people as shorthand for binary, but the machine itself works in binary.

Answer: C

Correct answer: FF, 255 decimal

A hexadecimal digit runs from 0 to F, so the largest two-digit value is FF, and

\[ FF_{16} = 15\times 16 + 15 = 255 \]

That is the same as saying two hex digits hold one byte, whose range is 0 to 255.