An exercise in sophisticated mathematics from “the team” this week.
What is 101010111110 binary in hexadecimal? 101010111110 from binary to hexadecimal is ABE. Here we show you how to write 0b101010111110 in hexadecimal and how to convert 101010111110 from base-2 to base-16.
To do this, first convert binary into decimal, then the resulting decimal into hexadecimal
- Start from one’s place in binary : multiply ones place with 2^0, tens place with 2^1, hundreds place with 2^2 and so on from right to left
- Add all the products we got from step 1 to get the decimal equivalent of given binary value.
- Then, divide decimal value we got from step-2 by 16 keeping notice of the quotient and the remainder.
- Continue dividing the quotient by 16 until you get a quotient of zero.
- Then just write out the remainders in the reverse order to get hexadecimal equivalent of decimal number.
First, convert 1010101111102 into decimal, by using above steps:
= 1010101111102
= 1 × 2110 × 2101 × 290 × 281 × 270 × 261 × 251 × 241 × 231 × 221 × 210 × 20
= 275010
Now, we have to convert 275010 to hexadecimal
2750 / 16 = 171 with remainder 14 (E)
171 / 16 = 10 with remainder 11 (B)
10 / 16 = 0 with remainder 10 (A)
Then just write down the remainders in the reverse order to get the answer, The binary number 101010111110 converted to hexadecimal is therefore equal to :
ABE (nickname for Abraham Lincoln – see the title)
So the unclued square in row 5 is B and, as I have said above, the one in row 8 is O (representing zero) … but even with the explanation, the process is Greek to me ….
Added to this, it seems that converting binary 101010111110 to decimal gives one 2750 – the number of the crossword – (101010111110)₂ = (1 × 2¹¹) + (0 × 2¹⁰) + (1 × 2⁹) + (0 × 2⁸) + (1 × 2⁷) + (0 × 2⁶) + (1 × 2⁵) + (1 × 2⁴) + (1 × 2³) + (1 × 2²) + (1 × 2¹) + (0 × 2⁰) = (2750)₁₀.
So the (1d) BINARY equivalent of row 8 is 2750 (the 6a, 37a) PUZZLE NUMBER and the (13a) HEXADECIMAL version of 2750 is ABE.
I’m certain minds more attuned to the subject will be able to expand on and refine this straggly interpretation.
Across
1 Piece of music about animal caught in railway carriage (6)
BOXCAR
BAR (piece of music) containing (about) OX (animal) + C (caught). Definition: an American railway carriage, usually at the end of a train, used for carrying luggage etc (boxes)
11 Angelic hordes holding divine flower? (5)
ICHOR
Hidden in (holding) angelIC HORdes. Ichor was the ethereal liquid flowing in the veins of the gods
12 Anarchic unit in Ambridge exhausted BBC (6)
AUNTIE
UNTI – anagram (anarchic) of unit in A + E (Ambridge without its content). Definition: affectionate name for BBC
14 Moon rocket fooled maestri (7)
ARTEMIS
Anagram (fooled) of maestri. Artemis II was the recent manned flight to the moon
16 Stars forgetting lines in Bodleian? (5)
LIBRA
LIBRARY (Bodleian) missing (forgetting RY (lines)
18 Ages of young cads regularly withheld (5)
YUGAS
Alternate letters (regularly withheld) of YoUnG cAdS. Definition: the four Hindu ages of the world
20 International plant produces iron framework (4,3)
TEST BED
TEST (international) + BED (plant, as a verb)
23 Auditor’s crossed river in Lycra (7)
SPANDEX
Homonym (auditor’s) of SPANNED (crossed) EXE (river)
25 Former PM eclipsed Macmillan or Thatcher (5)
NORTH
Hidden (eclipsed) in MacmillaN OR THatcher. Lord North (frequently used in crosswords) was PM from 1770 t0 1782
31 Patagonian hares about among ruins (5)
MARAS
A (about) inside (among) MARS (ruins)
32 Bad head? Sinusitis, perhaps (7)
ILLNESS
ILL (bad + NESS (head)
33 We induce an immune response in old giantess that’s ailing (11)
ISOANTIGENS
Anagram (ailing) of OLD GIANTESS
34 At home, judge Eastern recipe asking primarily for Ethiopian bread (6)
INJERA
IN (at home) + J (judge) +ERA (first letters – primarily – of Eastern Recipe Asking. Definition: a kind of bread made from tel in Ethiopia
35 Prove Marguerite’s content (5)
ARGUE
Hidden (content) in mARGUErita. Chambers gives “prove or indicate” as a definition of prove.
36 Attempts tests with much lower grade initially (6)
ESSAYS
ASSAYS (tests) with E (much lower grade than A) initially
Down
2 Ghastly chore yields money! (5)
OCHRE
Anagram (ghastly) of CHORE. Definition: money, from gold colour.
3 School secured ‘ten’ with someone at the helm (5)
COXED
COED (school) outside (secured) X (ten)
4 One nettles René d’Herblay (6)
ARAMIS
A (one) + RAMIS (grasses of the nettle family). Rene d’Herblay is Aramis, the second musketeer
5 Commercial I inserted in standard broadcast (7)
RADIATE
AD (commercial) + I inside (inserted into) RATE (standard)
7 Family men last to leave except when college opens (6)
UNCLES
S (last letter) to leave UNLESS (except) with C (college) opening it
8 Shell used to buy up independent business, investing money (5)
ZIMBI
Reverse (up, in a down clue) of I (independent) + BIZ (business) around (investing) M (money). Definition: a kind of cowrie used as money in Africa, word of Portuguese origin
9 Foolish old king ending in brown study (5)
LEARN
LEAR (foolish old king) + N (ending in brown
10 Awfully lean, needing way to put fat on (6)
ENLARD
ENLA – anagram (awfully) of LEAN + RD (road, or WAY)
15 Cover for Caesar to go absent from the front (4)
TOGA
TO + G + O – first letters (from the front) of Go Absent
17 Keen on badminton to some extent (4)
INTO
Hidden (to some extent) in badmINTOn
19 A man with an ark picked up dwarf buffalo (4)
ANOA
A +NOA -homonym (picked up) of NOAH (man with ark)
21 Concerning banishment from beating heart of Dixieland (7)
EXILIAN
Anagram (beating) of IXIELAN (Dixieland without outside letters). Definition: on the subject of exile – banishment
22 Cases of butter include cheese (4)
BRIE
Outside letters (cases) of ButteR and IncludE
23 One breaking into grin, as happy as Larry? (6)
SIMILE
I (one) inside (breaking into) SMILE (grin) . As happy as Larry being a simile
24 Snide about unknown film producer (6)
DISNEY
DISNE – anagram (about) of SNIDE + Y (unknown)
25 Ungulate wandering in Gaul (6)
NILGAU
A nagram (wandering) of INGAUL. Definition: a large Indian antelope
26 Missing first love, statesman who keeps stocking (6)
HOSIER
HOOSIER (a native of Indiana – a States-man) without O (missing first love)
27 Orchards originally unaltered and used in floral arrangements (5)
OASIS
O (first letter – originally – of orchards) + AS IS (unaltered). Definition: a block of light permeable material used to hold flowers
28 Lives with right leg in fetters (5)
IRONS
IS (lives) outside (with … in) R (right) + ON (leg in cricket)
29 Injured miner isn’t prickly (5)
INERM
anagram (injured) of MINER. Definition: without thorns, or unarmed
30 Children, a bone of contention
ISSUE
Double definition
Thanks Prospero! Valiant effort on all the maths stuff. I admit I simply asked WolframAlpha to tell me the Hex and binary numbers for 2750 and filled in the unclued lights accordingly. For submission purposes I highlighted all of row 8 and the letters ABE.
Doc likes to refer to the Spectator setters as his “team” so I imagine this was a team effort in which case the clues achieved a good level of consistency. We may imagine that Cheesecracker (aka Monk), who we know is a professor of mathematics, may have had a hand in the construction!
Thanks to “the team”!