Diminished Radix Complement Calculator and Quiz

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Questions and Answers

What is the radix complement also known as for binary numbers?

2's complement

What is the diminished radix complement defined as for a number N in base r with n digits?

(r^n - 1) - N

For decimal numbers, what is the r value and the r - 1 value?

r = 10, r - 1 = 9

How is the 9's complement of a decimal number obtained?

By subtracting each digit from 9 Signup and view all the answers

What is the 1's complement of a binary number represented as?

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

If n = 4, what is the 1's complement of a binary number?

(1111)2 Signup and view all the answers

What is the 1's complement of the binary number 1011000?

0100111 Signup and view all the answers

Define the r's complement of an n-digit number N in base r.

r^n - N for N ⬆ 0 and 0 for N = 0 Signup and view all the answers

What is the 10's complement of the decimal number 2389?

7611 Signup and view all the answers

How is the 2's complement of binary 101100 calculated?

010100 Signup and view all the answers

How is the (r - 1)'s complement of octal or hexadecimal numbers obtained?

By subtracting each digit from 7 or F (15), respectively. Signup and view all the answers

Explain how to calculate the 10's complement of a number.

Leave all least significant 0's unchanged, subtract the first nonzero least significant digit from 10, and subtract all higher significant digits from 9. Signup and view all the answers

What is the 10's complement of 012398?

987602 Signup and view all the answers

How is the 10's complement of a number calculated?

By subtracting each digit (except the least significant one) from 9, and subtracting the least significant digit from 10. Signup and view all the answers

What is the 2's complement of 0110111?

1001001 Signup and view all the answers

How is the 2's complement of a binary number obtained?

By inverting all bits after the least significant 1 and leaving the least significant bit unchanged. Signup and view all the answers

What should be done if a binary number contains a radix point before finding the complement?

Remove the radix point temporarily, find the complement, then restore the radix point. Signup and view all the answers

How is the 10's complement different from the 2's complement?

The 10's complement involves subtracting each digit from 9 (except the least significant one), while the 2's complement inverts all bits after the least significant 1. Signup and view all the answers

Study Notes

Radix Complement

The radix complement is also known as the two's complement for binary numbers.

Complement Definitions

The diminished radix complement of a number N in base r with n digits is defined as (r^n - 1) - N.
For decimal numbers, r = 10 and r - 1 = 9.

Complement Calculations

The 9's complement of a decimal number is obtained by subtracting each digit from 9.
The 1's complement of a binary number is represented as the bit-wise inversion of the number, i.e., 0 becomes 1 and 1 becomes 0.
If n = 4, the 1's complement of a binary number is calculated by inverting each bit of the 4-bit number.
The 1's complement of the binary number 1011000 is 0100111.

Radix Complement Calculations

The r's complement of an n-digit number N in base r is defined as r^n - N.
The 10's complement of the decimal number 2389 is 7611.
The 2's complement of binary 101100 is calculated by inverting each bit and adding 1, resulting in 0100110.
The (r - 1)'s complement of octal or hexadecimal numbers is obtained by subtracting each digit from (r - 1).

Calculating Complements

The 10's complement of a number is calculated by subtracting each digit from 9 and adding the carry to the next digit.
The 10's complement of 012398 is 987602.
The 2's complement of a binary number is obtained by inverting each bit and adding 1.
The 2's complement of 0110111 is 1001000.

Special Cases

If a binary number contains a radix point, it should be ignored before finding the complement.
The 10's complement and 2's complement differ in their calculation methods and bases.

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Description

Test your knowledge on radix complement and diminished radix complement. Learn about 2's complement, 1's complement, 10's complement, 9's complement, and how to calculate diminished radix complements for different bases.