157 in Binary

Decimal 157 in binary conversion provides the detailed information on what is the binary equivalent of (157)10, and the step-by-step work for how to convert the decimal (base-10) number 157 to its binary (base-2) equivalent.

(157)10 in binary is equal to:
(157)₁₀ = (?)₂
Perform successive MOD-2 operation for decimal 157, and mark the initial remainder as LSB and the final remainder as MSB as like the below.

157 MOD-2	157 / 2 = 78	Remainder is 1 → LSB
78 MOD-2	78 / 2 = 39	Remainder is 0
39 MOD-2	39 / 2 = 19	Remainder is 1
19 MOD-2	19 / 2 = 9	Remainder is 1
9 MOD-2	9 / 2 = 4	Remainder is 1
4 MOD-2	4 / 2 = 2	Remainder is 0
2 MOD-2	2 / 2 = 1	Remainder is 0
1 MOD-2	1 / 2 = 0	Remainder is 1 → MSB

Arrange the remainders from MSB to LSB forms the binary equivalent of 157.
157₁₀ = 10011101₂

Hence,
157 in binary is 10011101

where,
157₁₀ is the given decimal number,
10 in 157₁₀ represents the base-10 or decimal number system,
10011101₂ is the binary equivalent of the decimal 41,
2 in 10011101₂ represents the base-2 or binary number system.

Important Notes: (157)10 in Binary
The below are some of the important notes to be remembered while converting the base-10 number 157 into a binary number.

1. The initial or first remainder while performing MOD-2 operation for 157 is a Least Significant Bit (LSB).
2. The last remainder while performing MOD-2 operation for 157 is a Most Significant Bit (MSB).
3. The remainders of MOD-2 operation for 157 should be written from MSB to LSB to form the binary equivalent for the given decimal number (157)10.