Developer Bases

Decimal to binary

Decimal value

Binary 10101010

Divide by two, keep the remainders

The same number elsewhere

Decimal 170

Binary, grouped 1010 1010

Octal 252

Hexadecimal AA

Bits needed 8

Note

Grouped into nibbles · four bits per hex digit

The same number in each base

Decimal	Binary	Octal	Hex
0	0	0	0
1	1	1	1
8	1000	10	8
10	1010	12	A
15	1111	17	F
16	10000	20	10
64	1000000	100	40
100	1100100	144	64
255	11111111	377	FF
256	100000000	400	100
1024	10000000000	2000	400
65535	1111111111111111	177777	FFFF

Divide repeatedly by two and read the remainders backwards. 170 gives 10101010. Alternatively subtract the largest power of two that fits and repeat: 170 − 128 − 32 − 8 − 2 = 0.

How to convert decimal to binary

1 Enter the decimal number.

2 Read the binary, both run together and grouped into nibbles.

3 Check the bits row to see how many bits it needs.

4 Use the grouped form when writing it down — it is far easier to check.

The subtraction method is faster by hand than repeated division. Write down the powers of two above your number, then work down: does 128 fit in 170? Yes, so write 1 and subtract, leaving 42. Does 64 fit in 42? No, write 0. Does 32? Yes, and so on. It produces the digits left to right in one pass rather than in reverse.

Questions

What is 10 in binary? −

1010.

What is the fastest way by hand? +

How many bits for 1000? +

Why group the digits? +

Can binary have a decimal point? +

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