Question

Determine the binary encoding for a system that uses two’s complement of the base-10
quantities negative six and six for a digital system where all binary numbers are represented by four bits, one where all numbers are represented by eight bits (one byte).

Answer 1

Answer:

4 bits:

6 = 0110

-6 = 1010

8 bits:

6 = 00000110

-6 = 11111010

Explanation:

2's complement is easier to implement, because it only has one representation of 0 and starts counting backwards from the highest number you can represent with the available bits.

e.g.,

7 = 0111

6 = 0110

5 = 0101

4 = 0100

3 = 0011

2 = 0010

1 = 0001

0 = 0000

-1 = 1111

-2 = 1110

-3 = 1101

-4 = 1100

-5 = 1011

-6 = 1010

Answer 2

For 4 bits:

1. -6 = 0110
2. 6 = 1010

For 8 bits (1 byte):

1. -6 = 0000 + 0110 = 00000110
2. 6 = 1111 + 1010 = 11111010

What is binary encoding?

Binary encoding can be defined as a standard technique that is designed and developed to convert data in plain text (source alphabets) to a form that is easily used by different operating systems (OS), especially through the use of a binary digit (bit) or two-symbol system.

The two’s complement of base-10.

In Computer programming, two's complement of base-10 is generally easier to implement because it has a single representation of 0 only.

Decimal      Two’s Complement      Decimal      Two’s Complement

    0                       0000                        0                        0000

    1                       1111 1111                       -1                      0000 0001

    2                      1111 1110                      -2                    0000 0010

    3                      1111 1101                      -3                    0000 0011

    4                      1111 1100                     -4                    0000 0100

    5                      1111 1011                      -5                    0000 0101

    6                      1111 1010                     -6                    0000 0110

    7                      1111 1001                     -7                    0000 0111

    8                      1111 1000                    -8                    0000 1000

For 4 bits:

-6 = 0110

6 = 1010

For 8 bits (1 byte):

-6 = 0000 + 0110 = 00000110

6 = 1111 + 1010 = 11111010

Read more on binary encoding here: https://brainly.com/question/5381889