Question:

Convert the following numbers as asked :

1. Convert 756 (10) to an equivalent binary.
2. Convert 1.0125 (10) to an equivalent binary.
3. Convert 10110111 (2) to an equivalent decimal.
4. Convert 1011111111100111(2) to an equivalent hexadecimal.
5. Convert 49AF(16) to an equivalent binary.

A. )  756 (10) to Binary:

756 ÷ 2 = 378 remainder 0
378 ÷ 2 = 189 remainder 0
189 ÷ 2 = 94 remainder 1
94 ÷ 2 = 47 remainder 0
47 ÷ 2 = 23 remainder 1
23 ÷ 2 = 11 remainder 1
11 ÷ 2 = 5 remainder 1
5 ÷ 2 = 2 remainder 1
2 ÷ 2 = 1 remainder 0

Ans: 756 (10) = 1011110100 (2)

B. ) 1.0125 (10) to Binary:

Convert the integer part first:

1 in binary = 0001

Convert the fractional part by multiplying by 2 and noting the integer part repeatedly

0.0125 * 2 = 0.025 (integer part = 0)
0.025 * 2 = 0.05 (integer part = 0)
0.05 * 2 = 0.1 (integer part = 0)
0.1 * 2 = 0.2 (integer part = 0)
0.2 * 2 = 0.4 (integer part = 0)
0.4 * 2 = 0.8 (integer part = 0)
0.8 * 2 = 1.6 (integer part = 1)

Combine the integer parts obtained

Ans: 1.0125 (10) = 1.000001 (2)

C.) 10110111 (2) to Decimal:

Multiply each binary digit by 2n2^n2n, where $n$ is its position from right to left (starting from 0):

1 * 2^7 + 0 * 2^6 + 1 * 2^5 + 1 * 2^4 + 0 * 2^3 + 1 * 2^2 + 1 * 2^1 + 1 * 2^0
= 128 + 0 + 32 + 16 + 0 + 4 + 2 + 1
= 183 (10)

D.) 1011111111100111 (2) to Hexadecimal:

Split the binary number into groups of 4 bits from right to left:

1011 1111 1110 0111

Convert each group into hexadecimal:

1011 = B
1111 = F
1110 = E
0111 = 7

Combine the hexadecimal values:

1011111111100111 (2) = 5FF7 (16)

E.) 49AF (16) to Binary:

Convert each hexadecimal digit into its 4-bit binary equivalent:

4 = 0100
9 = 1001
A = 1010
F = 1111

Combine the binary digits:

49AF (16) = 0100100110101111 (2)