Binary game

This binary game trains the one skill every binary question needs: knowing what each bit of a byte is worth. Flip eight bits to make a decimal number, read a byte as decimal, or read it as two hex digits. Each round is 10 questions against the clock, the questions get harder as the round goes on, and your best time for each mode stays in this browser.

The place values of a byte

Every bit is worth twice the bit to its right. A byte's value is the sum of the place values that sit above a 1, so the row above is 64 + 8 + 2 = 74. To go the other way, take the biggest place value that fits, subtract it, and repeat: 100 is 64 + 32 + 4, which is 01100100. The binary numbers lesson explains why computers count this way, and the binary converter converts any number with the steps shown.

Tricks that make you faster

Learn the powers of two by heart up to 128; everything else is adding. Spot the halves: the top bit alone is 128, so any byte starting with 1 is at least 128 and any byte starting with 0 is at most 127. A byte of all ones is 255, so a number like 254 is quickest as 255 minus 1: every bit set except the last. Odd numbers always end in 1. For hex, never convert through decimal: split the byte into two nibbles of four bits and read each one as a digit from 0 to F, so 1010 0101 is A5. The hexadecimal lesson has the full nibble table, and the hex calculator does arithmetic in base 16.

Where the bits come from

A bit in a real computer is a wire that is either at the supply voltage (1) or at ground (0). In digiwleea you build those wires yourself: start from transistors, make the gates, then an adder that adds two bytes the same way you do in this game, bit by bit with a carry. The binary addition calculator shows that carry step by step, and two's complement shows how the same eight bits hold negative numbers.

Frequently asked

How do you play the binary game?

Press Start a round. In Make the number, a decimal number appears and you flip the eight bits until their place values add up to it. In Binary to decimal and Binary to hex, eight bits appear and you type their value. Each round has 10 questions and a timer, and they get harder as the round goes on.

How do you convert binary to decimal quickly?

Learn the eight place values of a byte: 128, 64, 32, 16, 8, 4, 2 and 1. Add the place values that sit above a 1 and skip the rest. For 01001010 that is 64 + 8 + 2 = 74.

How do you make a decimal number in binary?

Start with the biggest place value that fits, set that bit and subtract it, then repeat with what is left. For 100: 64 fits (36 left), 32 fits (4 left), 4 fits (0 left), so 100 is 01100100.

How do you read a byte in hexadecimal?

Split the eight bits into two groups of four. Each group is one hex digit from 0 to F: 0000 is 0, 1001 is 9, 1010 is A and 1111 is F. So 0011 1111 is 3F.

What is the largest number 8 bits can hold?

255, when all eight bits are 1: 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255. Eight bits have 256 patterns, from 0 to 255, which is FF in hex.

Is this the Cisco Binary Game?

No. It is digiwleea's own free binary game with a similar idea, converting between 8-bit binary and decimal against the clock, plus a hex mode. It is not made by or affiliated with Cisco.