(BABA)16 in hexadecimal is what in octal?

Concept

To convert a hexadecimal number to octal, do not convert digit-by-digit directly — the two bases do not align (16 = 24, 8 = 23). Route through binary: each hex digit expands to exactly 4 binary bits; then regroup the whole binary string into bundles of 3 bits from the right, and each 3-bit bundle is one octal digit.

Application

Step through (BABA)16 using hex = 4 bits per digit:

1. B = 1011, A = 1010, B = 1011, A = 1010, so the binary string is 1011 1010 1011 1010.

2. Write it as one run: 1011101010111010 (16 bits). For octal, group in 3s from the right; 16 is not a multiple of 3, so pad two zeros on the left to make 18 bits: 001 011 101 010 111 010.

3. Read each 3-bit group as an octal digit: 001=1, 011=3, 101=5, 010=2, 111=7, 010=2.

4. Concatenate: 135272.

Cross-check

Independent decimal check: (BABA)16 = 11x163+10x162+11x16+10 = 45056+2560+176+10 = 47802. And (135272)8 = 1x85+3x84+5x83+2x82+7x8+2 = 32768+12288+2560+128+56+2 = 47802. Both equal 47802, confirming the result.