# Counting to 100 in Base 4

Can you count to 100 in base 4?
Quiz by Stef2
Rate:
Last updated: August 26, 2019
You have not attempted this quiz yet.
 First submitted June 28, 2019 Times taken 40 Average score 42.6% Report this quiz Report
10:00
Base 10
0
/ 101 guessed
The quiz is paused. You have remaining.
Scoring
You scored / = %
This beats or equals % of test takers also scored 100%
The average score is
Keep scrolling down for answers and more stats ...
 Base 10 Base 4 0 0 1 1 2 2 3 3 4 10 5 11 6 12 7 13 8 20 9 21 10 22 11 23 12 30 13 31 14 32 15 33 16 100 17 101 18 102 19 103 20 110 21 111 22 112 23 113 24 120 25 121 26 122 27 123 28 130 29 131 30 132 31 133 32 200 33 201 34 202 35 203 36 210 37 211 38 212 39 213 40 220 41 221 42 222 43 223 44 230 45 231 46 232 47 233 48 300 49 301 50 302 51 303 52 310 53 311 54 312 55 313 56 320 57 321 58 322 59 323 60 330 61 331 62 332 63 333 64 1000 65 1001 66 1002 67 1003 68 1010 69 1011 70 1012 71 1013 72 1020 73 1021 74 1022 75 1023 76 1030 77 1031 78 1032 79 1033 80 1100 81 1101 82 1102 83 1103 84 1110 85 1111 86 1112 87 1113 88 1120 89 1121 90 1122 91 1123 92 1130 93 1131 94 1132 95 1133 96 1200 97 1201 98 1202 99 1203 100 1210
+2
Level 69
Jun 28, 2019
Here's how to count in base 4 for all who need help! Each digit in base ten is the value of that number times 4 to the power of the place of the digit (with ones being the 0th place, tens being the 1st place and so on). So a 2 in the ones place is equivalent to 2*4^0 (or just 2). A 3 in the hundreds place is equivalent to 3*4^2 (or 48). The final number in base ten is adding the converted numbers. Converting from base ten to base four is the complete opposite.

I probably explained that horribly, so let me use examples. Say we want to convert 67 to base 4. The highest power of four that can go into 67 is 4^3 (64). Only one 64 can go into 67, so the thousands digit(what 4^3 will be) is 1. 67 - 64 leaves 3. 4^2 (16) and 4^1 (4) are both greater than 3 so the hundreds and tens place will remain at 0. 4^0 (1) however can go into 3 three times meaning the ones digit will be 3. That leaves our final answer to be 1003.

I hope I didn't miserably fain at explaining, but here you go!

+1
Level 61
Jun 28, 2019
This explains it very well!