Binary Octal Decimal Hexadecimal Quiz & Flashcards

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Questions and Answers

What is the process of converting a decimal number to hexadecimal?

Repeatedly divide the decimal integer by 16 and each remainder is a hex digit in the translated value.

How is the decimal number 422 converted to hexadecimal?

422 = (1A6)16

How would you convert the decimal number 139 to octal (Radix 8)?

139 = (213)8

Explain the process of representing fractions in a radix r number system.

A number Nr in radix r can have a fraction part: Nr = dn-1dn-2 … d1d0 where 0 ≤ di < r. Signup and view all the answers

What is the significance of the remainder when converting from decimal to hexadecimal?

Each remainder obtained during division is a hex digit in the translated value. Signup and view all the answers

Explain the process of converting fractions from Binary to Hexadecimal.

Integer part: right to left, Fractional part: left to right Signup and view all the answers

How many bits are grouped to form a hex digit?

4 bits Signup and view all the answers

What is the simplified method for converting fractions between Binary, Octal, and Hexadecimal?

Start at the radix point, convert integer part from right to left, and fractional part from left to right Signup and view all the answers

Explain why 2 should be represented as (10)2 in binary when adding 1 + 1.

To follow binary arithmetic rules Signup and view all the answers

What is the widely used representation for signed numbers?

2's complement Signup and view all the answers

How are signed numbers represented in 2's complement?

n-bit number, sign bit, and bit n-2 Signup and view all the answers

What is the standard way to represent signed integers in computers?

2’s Complement Representation Signup and view all the answers

How is the 2’s complement of a binary number calculated?

Given a binary number A, the 2’s complement of A = (1’s complement of A) + 1 Signup and view all the answers

What is the range of represented values in 2’s complement form for n bits?

-2^(n-1) to +(2^(n-1) - 1) Signup and view all the answers

What is the property of the 2’s complement in relation to the original number?

The 2’s complement of the 2’s complement of A is equal to A Signup and view all the answers

How can subtraction be converted into addition using 2’s complement?

A - B = A + (2’s complement of B) Signup and view all the answers

What happens in the case of overflow when adding signed integers?

Overflow indicates that the signed sum is out of range Signup and view all the answers

How is sign extension performed in binary numbers?

Move the number into the lower-significant bits and fill the remaining higher bits with the sign bit Signup and view all the answers

What is the significance of the final carry in 2’s complement addition?

The final carry is ignored Signup and view all the answers

What is the key advantage of using 2’s complement for subtraction?

The same adder can be used for both addition and subtraction Signup and view all the answers

How can overflow be detected in binary addition?

Cn-1 does not equal Cn Signup and view all the answers

Study Notes

Number System Conversions

To convert a decimal number to hexadecimal, divide the decimal number by 16 and keep track of the remainders; the remainders will be the hexadecimal digits.
The decimal number 422 is converted to hexadecimal by dividing it by 16: 422 ÷ 16 = 26 with a remainder of 10, and 26 ÷ 16 = 1 with a remainder of 10, so the hexadecimal representation is A6.
To convert the decimal number 139 to octal, divide it by 8: 139 ÷ 8 = 17 with a remainder of 3, and 17 ÷ 8 = 2 with a remainder of 1, so the octal representation is 213.

Fraction Representation

In a radix r number system, fractions are represented by dividing the fractional part by r and keeping track of the remainders; the remainders will be the digits of the fractional part.
The significance of the remainder when converting from decimal to hexadecimal is that it determines the next hexadecimal digit.

Binary, Octal, and Hexadecimal Conversions

When converting fractions from binary to hexadecimal, group the binary digits into sets of 4 and convert each set to a hexadecimal digit.
4 binary digits are grouped to form a hexadecimal digit.
The simplified method for converting fractions between binary, octal, and hexadecimal is to convert the fraction to one system and then convert the result to the desired system.

Binary Number Representation

In binary, 2 should be represented as (10)2 because the binary system can only represent two values: 0 and 1.
The widely used representation for signed numbers is 2's complement.
Signed numbers are represented in 2's complement by inverting the bits and adding 1.
The standard way to represent signed integers in computers is using 2's complement.

2's Complement Operations

The 2's complement of a binary number is calculated by inverting the bits and adding 1.
The range of represented values in 2's complement form for n bits is -2^(n-1) to 2^(n-1) - 1.
The property of the 2's complement in relation to the original number is that the sum of the original number and its 2's complement is 2^n.
Subtraction can be converted into addition using 2's complement by adding the 2's complement of the subtrahend to the minuend.
In the case of overflow when adding signed integers, the result will be incorrect.
Sign extension is performed in binary numbers by copying the sign bit (most significant bit) to the left to extend the number.
The final carry in 2's complement addition indicates an overflow.
The key advantage of using 2's complement for subtraction is that it allows for efficient and simple implementation.
Overflow can be detected in binary addition by checking the carry bit.

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Description

Learn how to convert fractions between Binary, Octal, and Hexadecimal in a simplified way by starting at the radix point. Practice grouping bits into hex or octal digits and converting integer and fractional parts step by step.