Convert the following decimal numbers to binary: a. 55
b. 32
c. 82
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Convert the following decimal numbers to binary: a. 55
b. 32
c. 82
Sure! Let’s convert each decimal number to binary step by step.
### a. Decimal 55 to Binary
1. Divide the number by 2 and write down the remainder.
2. Continue dividing the quotient by 2 until it reaches 0.
3. The binary representation is the remainders read from bottom to top.
Calculation:
– 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: 55 in binary is 110111.
### b. Decimal 32 to Binary
Calculation:
– 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: **32 in binary is