The sixth design in the “British Inventors and Scientists” collection is not a sock… XNOR is a nod to Boolean Algebra, introduced by George Boole, English mathematician and logician during the 19th century.

Like all logical functions, XNOR is described by a truth table. The XNOR pattern in the body of the hat is my knit/purl interpretation of that truth table (rounds 1 and 2 are input, round 3 is output; true = k, false = p).

Bonus: The hat is reversible… and the “wrong side” is the knit/purl representation of XOR, the logical complement to XNOR. Isn’t it magical?

Sizing
Newborn (Baby, Toddler, Child, Adult S/M, Adult L)
To fit head circumference: 36 (41, 46, 51, 56, 61) cm / 14 (16, 18, 20, 22, 24)“
with approximately 5 cm (2”) negative ease

Yarn requirement
100% wool, DK weight:
55 (75, 100, 125, 155, 190) m / 60 (82, 109, 137, 170, 208) yds approximately for a hat without pompom.

You will need a little extra if you choose to make a pompom (5-15g depending on the size and fluffiness of the pompom).

Samples shown:

• Child size - Charcoal and lime: Ripples Crafts Merino Double Knitting in shade Assynt Peat and Slice of Lime
• Adult S/M - Blue/Grey: Baa Ram Ewe Dovestone DK, in shade Aire
• Toddler - Light blue: John Arbon Knit by Numbers DK, in shade 84 Kbn

Needles and Notions

• 4 mm (US 6) needles - Or size required to achieve gauge. ― circular or DPNs to work small diameter in the round
• 3.25 mm (US 3) needles
• Darning needle
• Stitch Marker
• Crochet hook and waste yarn
• (Optional) pompom-maker, or tools for your preferred method to make a pompom

Gauge
27 sts and 38 rows / 10cm (4 in) in XNOR pattern worked in the round, with smaller needles.