Question

The decimals to this

Answer 1

A conversion of the given Binary to its Decimal equivalent include the following;

1. 61
2. 48
3. 5
4. 3
5. 45
6. 34
7. 70
8. 39

Part 1.

In this exercise, we would convert the given number 111101 in base 2 to base 10 and this can be done as follows:

`111101_2 = 1 * 2^5 + 1 * 2^4 + 1 * 2^3 + 1 * 2^2 + 0 * 2^1 + 1 *2^0\\\\111101_2 = 32+16+8+4+1+0\\\\111101_2 = 61`

Part 2.

We would convert the given number 110000 in base 2 to base 10 and this can be done as follows:

`110000_2 = 1 * 2^5 + 1 * 2^4 + 0 * 2^3 + 0 * 2^2 + 0 * 2^1 + 0 *2^0\\\\110000_2 = 32+16+0+0+0+0\\\\110000_2 = 48`

Part 3.

We would convert the given number 000101 in base 2 to base 10 and this can be done as follows:

`000101_2 = 0 * 2^5 + 0 * 2^4 + 0 * 2^3 + 1 * 2^2 + 0 * 2^1 + 1 *2^0\\\\000101_2 = 0+0+0+4+1+0\\\\000101_2 = 5`

Part 4.

We would convert the given number 000011 in base 2 to base 10 and this can be done as follows:

`000011_2 = 0 * 2^5 + 0 * 2^4 + 0 * 2^3 + 0 * 2^2 + 1 * 2^1 + 1 *2^0\\\\000011_2 = 0+0+0+0+2+1\\\\000011_2 = 3`

Part 5.

We would convert the given number 101101 in base 2 to base 10 and this can be done as follows:

`101101_2 = 1 * 2^5 + 0 * 2^4 + 1 * 2^3 + 1 * 2^2 + 0 * 2^1 + 1 *2^0\\\\101101_2 = 32+0+8+4+1+0\\\\101101_2 = 45`

Part 6.

We would convert the given number 100010 in base 2 to base 10 and this can be done as follows:

`100010_2 = 1 * 2^5 + 0 * 2^4 + 0 * 2^3 + 0 * 2^2 + 1 * 2^1 + 0 *2^0\\\\100010_2 = 32+0+0+0+2+0\\\\100010_2 = 34`

Part 7.

We would convert the given number 1000110 in base 2 to base 10 and this can be done as follows:

`1000110_2 = 1 * 2^6 + 0 * 2^5 + 0 * 2^4 + 0 * 2^3 + 1 * 2^2 +1 * 2^1 + 0 *2^0\\\\1000110_2 = 64+0+0+0+4+2+0\\\\100010_2 = 70`

Part 8.

We would convert the given number 100111 in base 2 to base 10 and this can be done as follows:

`100111_2 = 1 * 2^5 + 0 * 2^4 + 0 * 2^3 + 1 * 2^2 + 1 * 2^1 + 1 *2^0\\\\100111_2 = 32+0+0+4+2+1\\\\100111_2 = 39`