Convert the following decimal number into binary. please give full answer a) (128)10 b) (55)10 c) (173)10 d) (39)10 please give full answer
The Correct Answer and Explanation is:
To convert a decimal number to binary, we divide the number by 2 and record the remainder at each step. The binary representation is the sequence of remainders read from bottom to top.
a) (128)₁₀ to binary:
- 128 ÷ 2 = 64, remainder 0
- 64 ÷ 2 = 32, remainder 0
- 32 ÷ 2 = 16, remainder 0
- 16 ÷ 2 = 8, remainder 0
- 8 ÷ 2 = 4, remainder 0
- 4 ÷ 2 = 2, remainder 0
- 2 ÷ 2 = 1, remainder 0
- 1 ÷ 2 = 0, remainder 1
Reading the remainders from bottom to top, we get the binary equivalent of 128 as 10000000.
b) (55)₁₀ to binary:
- 55 ÷ 2 = 27, remainder 1
- 27 ÷ 2 = 13, remainder 1
- 13 ÷ 2 = 6, remainder 1
- 6 ÷ 2 = 3, remainder 0
- 3 ÷ 2 = 1, remainder 1
- 1 ÷ 2 = 0, remainder 1
Reading the remainders from bottom to top, we get the binary equivalent of 55 as 110111.
c) (173)₁₀ to binary:
- 173 ÷ 2 = 86, remainder 1
- 86 ÷ 2 = 43, remainder 0
- 43 ÷ 2 = 21, remainder 1
- 21 ÷ 2 = 10, remainder 1
- 10 ÷ 2 = 5, remainder 0
- 5 ÷ 2 = 2, remainder 1
- 2 ÷ 2 = 1, remainder 0
- 1 ÷ 2 = 0, remainder 1
Reading the remainders from bottom to top, we get the binary equivalent of 173 as 10101101.
d) (39)₁₀ to binary:
- 39 ÷ 2 = 19, remainder 1
- 19 ÷ 2 = 9, remainder 1
- 9 ÷ 2 = 4, remainder 1
- 4 ÷ 2 = 2, remainder 0
- 2 ÷ 2 = 1, remainder 0
- 1 ÷ 2 = 0, remainder 1
Reading the remainders from bottom to top, we get the binary equivalent of 39 as 100111.
Summary:
- (128)₁₀ = 10000000₂
- (55)₁₀ = 110111₂
- (173)₁₀ = 10101101₂
- (39)₁₀ = 100111₂
Explanation:
To convert a decimal number to binary, we repeatedly divide the number by 2 and track the remainders. Each division step gives us the next least significant bit (from right to left). The process stops when the quotient reaches 0. The binary number is formed by reading the remainders in reverse order, from the last division to the first.
